From ba53d4835816a4da48b893d8cad82e4c42f37493 Mon Sep 17 00:00:00 2001 From: Bertrand Benjamin Date: Sun, 1 May 2022 09:14:28 +0200 Subject: [PATCH] =?UTF-8?q?Feat:=20fin=20des=20exercices=20sur=20le=20chap?= =?UTF-8?q?itre=20des=20vecteurs=20et=20des=20coordonn=C3=A9es?= MIME-Version: 1.0 Content-Type: text/plain; charset=UTF-8 Content-Transfer-Encoding: 8bit --- .../1E_coordonnees.pdf | Bin 27735 -> 27735 bytes .../2E_operation.pdf | Bin 28365 -> 28365 bytes 2nd/18_Vecteur_et_coordonnées/3E_norme.pdf | Bin 19966 -> 19966 bytes .../4B_determinant_colinearite.pdf | Bin 29875 -> 29804 bytes .../4B_determinant_colinearite.tex | 4 +- .../4E_determinant_colinearite.pdf | Bin 0 -> 24790 bytes .../4E_determinant_colinearite.tex | 18 ++++++ 2nd/18_Vecteur_et_coordonnées/exercises.tex | 58 +++++++++++++++++- 2nd/18_Vecteur_et_coordonnées/index.rst | 8 ++- 9 files changed, 83 insertions(+), 5 deletions(-) create mode 100644 2nd/18_Vecteur_et_coordonnées/4E_determinant_colinearite.pdf create mode 100644 2nd/18_Vecteur_et_coordonnées/4E_determinant_colinearite.tex diff --git a/2nd/18_Vecteur_et_coordonnées/1E_coordonnees.pdf b/2nd/18_Vecteur_et_coordonnées/1E_coordonnees.pdf index 07b4f8788e3c006e688d9076a4d979bf5f29b93b..46a57c724c943bfd8a85536989d3cdbf809c5bc1 100644 GIT binary patch delta 188 zcmcb9gYo(e#tr=m?xuPMnhN^PMX8A;nfZAxi6yBD8ZK5w21Z5(rUr%vmWD=##@Yr( z>IMetKy|+PDcF@vzLwx21T;%QBP2CK!6&mURRLtiW`o4poUTsJj&81&W=?MAZidDd mZU*MAj>Zjdl!3Y3}LozG? delta 188 zcmcb9gYo(e#tr=m?#6mXnhN^PMX8A;nfZAxi6yBD8ZK5w21Z5(CdLMa7C>yIZD6Es zV4x0E=bN8`UCHEY2_8Z~vlKK!QX>?6GRsmGfMytOHb|V!>1ycWWNcz$VeVvMV(wz@ lVq|P)>11kd>1u9bZ0c&^Y^PvjNl;1b6wGb147Xs2L9K*{DeK0=HD#b+-T delta 181 zcmex2oAKXl#tjc$+>P~&G!^uni&7IyGV}9X5=&AQG+eBV42+BnOpFZ-Er8fi+rUWO zz(5_S&Nn{=yOPNot{y@_vlKK!QX>?6GRsmGfMytOZgSONcQP`tFflhVFf(&8H#IkQ gbv81wbaApYcQ!P2H8(LaaKQ+qUi8*tV^XZQHhO+nMj5=UHo>>SeFMNrIue7D?@YzwjFVr51%tLOV^r5k}6#X_E*=j?H0avD2a321L`#n8+ zbrNi2zA>~W2fgBl=>}MlL*>6O`V1fT^uUOGJNLc-Xk7NJ_NI*}ueXXgte-KZ7joav z2U8z%?EE|&+~U)f$)bq4zFi={zR?07r7gJK>C*0OUmrbyuWtk=<6B(eayECRob1P{ zw~rgMx$OkSbbm@df2-$wqx)u_b@--z(~&&Qwn6pG>=bolyz87>m45qu94*K#9Y!~- z8`-MDm`s>ueZ7-P|9me@*?oCuBmIgSSUAD6WFI$rx15y@4D9)FdVM;s!%dbdMUa;y z!Ou?__Tr2Nwttrydg}K{R#@fGOlLU;I>l(DdeHUj>=kq-$D`3X+y(U9E9Z%XJ^sV} z9s~(4!KsE>v*773N{oXTgyiA9dD6jUoRFGUHs);&LU_ykCs#13t0;~xHJ=zJ){842gt4B|iq+*W7(F#h1hec>|uU=Foypng_yEM8?I5Rq45TA&I}qRcA3l@jieLBYm)B9MDAEWFMm{@a&=g7ue*Xq=`W z;7Jw%=&>zhbp43Frv0F#9Pm9om+JVqQkG`oGbu$@O>SO)5U@PwCJH1k< zmZ^Tv;3rD#mea~LrOO~WDYQYg0E_HUd-^(in7sq-V94&Fw5RxgzRC(YeJJf<9@#F%Bg*|Jr!E)p@! z#HAn;nJwKU0Q{bvt>!&QOM6mBAa+j4X${-X3=;|=TL?)KEYpFXN)%C>LyO7*+kJ5d z(lti$$w?`>yRRMr@HH#J=VppbS9s7!(W;=5^s!)IO82kDSz$I|cjEuHb5h%mMz;I? zIyo6brw`F`Kdd9=guk$);Cv=+67H!nQ}m;3JCv#*qmWP$iLHN4k+5;EF$KHC zX@8)-lYKfK;J~-!ZU*O71D-R%a%f_JCYIGlZKx@nUHWY~U|E72AuC7+hgo`)l6D8eE5mrhEp8BbZNpf=Ehtv{;2GaRhZVq&n;LD? zdivyTSVH~sU>2vNXIQQ8H<*?0hfhwd%9a_af;_jSePu#uZ4ioJCdFq=5H!|-xZ;7J(fQ@S^GdcZfenqkNF&k{**T@eCH@5==Wkr)tkNdm2*wsw#1o%*qw|^qDR1m? z#Z3XU4|p*LBc~5ek4;=VFze=dU3$xlP$lvlHx1w3(!822u=1+d71TTDCwr-{ z7ewlW{ChY2_W8({Uh{xsj2ANCyFx-2U}&H{@lY3rqDeW)XKo#mk=y#AkddFJYh<1m ziSd{*CnR>@K;9!^$#|uSM6OkuP0q2>Ovm&SkYj_<15sCz&Kflf)=>AGjyKh0pd*`xvub+^~RxZj61X4Zlyn{j*lm1{VgD zLIheO*or`-*_f9qPJ+J)f@s2V%Lzn_(CWt=LYc#^McrXDS$i0xO-C_tm%G7{wAfcg zjaWE7Y!Zf&GRnb}lbwGJWtx21jCwdr2rLEHV-H$7W@ZNq1$c*g&<1JpsnaDj&C8zU{8hY0;;L$fL|fK%6!kJ{?DZV z>=N^bWyT@rG+vcO7unmbN(80;vZ-HI)Bo0VQtuwD{+!Nou?P!zj;8=0MD(alb6n(^ zZc1r@UAkB0R~d^Qn8%AP+PiL@9uUQxZ+$Q*Nx;=Ai#LBb?BR-cUVEFws4$rR+Puovjbh?w&f~1%kGEGm{DEzVV7%zWrP zSk@ovoQ0h@ch(@`7ye=;HUWrbM`EG~Ze~iqYDW+c@q8%w#DIjJ{tVd!ug&z5uG{H>@{#D3IUJbt#}^@%A#?dq`G(_~ne>bUAe za4K9@bjzPs{ot7qHBC{Q=$b82Gd}m2<<(P>cueJD=~UiHrnc4bhrDPEMP8XTn{UDY zuO#mDKcFP=Xy?kTX3s-iIx?(OsHE_cwHKpxXZnfq3pNu3u6}nG#3E^&ZGK2sH*6}1 zUA2J)E+PhPJL@B-01d}roq;?RZ2%X`-o`E!HIq?K@x?cni(I2O;->7vaX=@0a?IOq z$!h&ywI)%DQfpluU-^@M-2-ZE>hWzQT~!XG%W@g;+&X63W*6KqJN@kZO9xIkXrUD| zK|!av9g3;es}mc91dmt_;Ni=-`BlBx89e(Qo~1xliI~F$*@U6jkC7@%yXtI_3dsIG zCFO&`?rp8b6@|eo^DL*GfN&nDgLyaT+j-mbZnOEte6w!Fg$FG)H>g?>s8H|Q2yU`FT7)|JH>kP8M5kUO zB?vw{M~TRYAi<|NRsr~MU+o_1%?uKV1S}!F#rDseyp-z6a=Mq{&NTpBQrIe*n^u=&( zzof#It#hQBGzGXt`m)sR=P{PT_0eP$%?ihYTWkKwK#V1dn8JR8*1x++*H&ZaUjQH# zc%c)$J8R{p;OQ4A)t)_Rl2VMC$tBh|$-+hG>3*D;CX^qf70AUTl17qh7y&)-sP@J_r?pz5{WN#Q}PGfycL+SF_L%B@J7=czNv(;HP= zhqv#V;v(aNl*HEcwR#FPUm2Y2{l)YbSlRo`+-e3V+OEmVHg%WOnZ?;+Zk?^BXZ;};RiGUI>*>omRnHSH#6Zl{WUq^N}_!dbb-1#|jg z*HrcP@LHN@b^{~Qiu(BqFRs$|kVF>ue`7fC1dAZrV&;U8zOAmshgNmU(1Vt(;Yvkz zXfP8$G92y1unYN(feS)Kr6x7BkK$}EchCrEQHzK$BHFRdbz-OrB(519HXo4A15M)G zTtY5|fu>VrfNs>B*E!hiVBwiNl?UBRO4B0EW(d;_fo1b75beLBf2}By78y*_s>pM* zl@^{NB`Y@*{FdWPzsd4Gn4ENj{86bUmo!OdeAo63kz{I0)#59xWg_Prt!cQ)kcwO~ z_^6gU22)yp6ml2=4s1cGE9fJ*xh-Hh+PX3`+lvb(c?MnxSJD;zjiXcj*BVMAKE1aE zwk6Ch5FGOQ7!a{-kdvk+%dqHe6!lHlO|>*SJEnlCsuJV)WWA$c8&Q!El#eJ|mN5!O zq&dJ{yhg=UbS~BUKC|r=or-3{Zb^E|JB>S2R$TZNovD%@DtvB-h9&ZnAjP#zmKuMLV3D ztUugVz?`&!FVIGPhK-a@G9R|3n~fNo3^CB1LmF(1Ot`Du3}K~JoXwjAcnHNfSdr;O z82{#E)JQOkHkXPv*^4%b5)JEABwYSb$uf}l2P8G}iYlHGa4=H|5+?j^GtQXENn##z zYez9&3dk}X*b@FL62nI!X2gx)+m{|%DZ@D&3!Bjlbn)FO4x&IPRkH?X)N8zPb!l?c z@UBj}oWPRqn9w=%SMU!-C@(!Tp-Xd&3Y|URItUw7 zWu?*Tx}lR*}0hjYMK7GF*dB0NIT9!ED5W0(n zR|nq*J~`C6t&w~HA z_Q4QKSz-J!{gjdBRJi+d!qx3`AMHf2gY!9Z#C4c?$Q5KXKEFlauF_voXe!r&_qS@W)iX6&ChGV zyV&KR>`i>ACb|fM39W!MI3IHVFniJ*^{oufXM4hP`Q7q`kEwP)3Kd?$Db7-gggP}A zC>)4EL+%ko(k*|{P7D2XyjgwP`;SF@PECY9uajb`cvn)K-9&!$pd-c_VrNNnE_%Zq zXx3qDg}`4{`aZ=>jL{IJW<`bk7D0tf1ZhIad8f&VJdlK@MkYY$phzqb3M0e9TtlSHRciY^90mA{3mY37!peF=T{zYc9mP44Z4-7c3fff?1sa$qw#x z-6m#SoLbJ-&=;0F(ZMJXyi7W~Nf9H6`I`G;kCfBt0x|Chw6`V2YF37s2~K^VQY-q# z7Trmr@OU1!4aOf8n@ld8tX<$Qro-kVDC7?O!ed}sTkCBLU`08*Hk&O8oF1Guv`Iz> zqLw()^X8wG(fC!Js~`1nOoQ`)VReA-Hrp)jmn?NhYuJ`^994W@erHkoc4%j2>%p8O zT}*{3RjJ>OkH$~vPVckkGP5`w|JqMhFO)ZJH`o6Nds08VMf|C4-+YQGr7xlWmqAPi zVK=rJzUDcVu5|ZJJY|F3)lpd3?w*qztdnAcVOgPVZ7EUX@n`uhp(b^UV0~!oX^8c6 zUB@zg-BU_qS!5BfreQSq2Mi>X%c3C`%LD;N-0T(XmrWyHbnAqn*@-%xQx0`zvGr&QIB|}!D$6yDK%N5hGpku%Iwc~WB0dP@3v?AQR zV9ttUMR?X)anM148g{(_83_fp-cV(RP7?b> zqMo4?&@b($AMov`D=U-~Yn%0l=!x0&E2PiPWo|HUm)HCaK4!G1Vxx3PU-=jsIiG+3 zO##ARd#N_aTZmpDw-CnwkPLZ1TB-81>*US+p?~=hq7G4q4--vS1lO$n`3K?m(XjB{jK0yQGU4qX+G~W)nXUI<& z-?jAJI}D!qoGfZ+!Ox#BDfv6Iv?@c#c2+IvCbEnwjbrY;$UDOxf5UoU(h1zUw~3|Z zj~-%hlyn2tRhu&N{O@oG!YHlB!wT)~k-}9puuF2LXE4G!qBxzj++PU?cbo*p^+Krl ziZJ!3E)uOURja(RMKcEt5QnG|lV&BId~)%|NUzc5;dv_;efvh+i!H9XK~}uB0^>6y zSk&m5TgP$Q^*U2gO0HNy@H)@Cty%NdPv=JNK4`51ny2!u}3X%mKK(TDQDoT8B4jd}C|e{BT&Wt$WrNG%-D z>HieYF(q5K0EpjtWohS_o@b9zv&a+p1%#0U&L_k4uVf$l*xDzAFCp8=gt_2wcQ$Nn zApuC-Lt}p8)jVT+y%k>a#MJek(MYIHU&qZlW&Y_&DM?Mp{(RDe3A#bD!#$IkoId4jKCV; z-%{w26F181WXPFyaya+;&Yr;HWct*FOA1V@>d}l5Qn~7)r}6by)cRjM*VuBl`kU!r zwbTidW0)1>8ws{ksO{V2YC0%Fd?|=R1Cy`hO#=5OfOk7!BvX=Jos4QQ`efkY#o5i1 z)hdp^>*m=&y~CRK5Ur2zC6yORp^$2%7BmJV*CV)(E7jp_ms)OHc2uy2+{j4%#<6vBv)7x!xIa^$ zFp@>P)>|F$u8XjxXgN-=wZZe|NY45o_D$N#rd#jMLvE#2-Z70eQ|RiS-$oeL_ol;!(n|ySpmQzH>ngY@`@?@5*H>UyeMs*?d5M7dm#jkXQbcPH&XqSG#q- zEfcnD-=E}&gbv|nkIg6}%t|V3%EwpWHPT!xbIw!R;HLN`Y-anfqq(7K zu!OGJKN~i(`HO%C+JX=H0gt%|F$4r5hZaUc*%h6%S)UM2=Bb3_;Amo3EVP9xiM^81 zIB&YOnrWs=xkefT`_nA~{emJ(HaxttVTgn}4CmD*0KK0~6fHCxTm42_*F;M@)u<@n z!X^{2upQM!O%b8I97}btzN46)MNnQN+bx{sS!bilQ}%Y}Ottk2lO|xQNmcNk*P5X= zi9`!A9itvtOZ<36u1U^Wr2kSpe|6WS8WokE>OfR(gG_VidWT(?Kh!+lhwy^Q%I0<< z4JQZRNY44dNcH9UHNy=|o>jG~N<08E(?6}K$GRxE|CdB92yIO!>V`^eg7z8}+NW2VW54ny?cMa~P;*8`x0 zm#0B^pgnFZd+kq}e%E<eo$NtIXZX_hF=c)v|P~g+l-U7m@Zyq|tQA$RTOb z&=m8!uCn$!B-pg(Y>Xc-igMuB43|Lr#-881d+{_O&Q~!_ZcilKqXtl+a!BV?WX{yi z9_o=&wxJ`Topqv4y9%Vl6-JHHt*NfsTyu0DORmjpky|;6mH&0#Nk#Q<`z;&%{u%?s z4XO4Ymo7I+W2Q>OmWG8#*GMiNsMHk9 zgoB3qB+2f^JhLY|oN-zzr7GELYbyHYwL5DH(+SCGmi0yH%)yuFPNxUzs-BLnF;ok* zn)QQGlaGukWKIdIOG&{mI?+JG7;TGP!`TH=&J^iEb@ zGl?eS6Wk$VspjN0Y0*Lo#(|`C8wvbu%W-sOQ8Uw`gA>t2R+uTxKg+;F=|@9ZW~~MY z;pDWO_)H6&_yn6lnYGthN>j6pgh`8%$#~Ha1_GgJ^d)kbFjSkcV@A{AzY$cdDuXS8 znFx&JysR*4{AQw$6raR60fDC~-%*AMR8uVdSuPuNT9^@kTc>_)F!Woqnq??P8>)tI z&h^v9aY>bMGHM;co(%(cl~jVImH<(=#U#=ekkhak(a`%ut^#c zvvbn7AjwA(OxPkyq@^$gkrS8~Q0SycuJt8|qS5QUH3r-@G*=rw;6T;twgf4A$r`9I z5KI}dU#et~1^Ks;2l%(4x6<)*c*geiyKpEMcGZePR-iMWSQvpBJLZIo&Wq0TgO-Hz zr>s3oJOy=De2ZDjfA~Hwr&t@1?zP3IW8<$OXYr z&bWUXR&*A!zfMm*WZFzKkMV2*ngzY;bW}UooeQcJ-FOU@2Q$LhN$H&8wdt>MriYds z?V4^jyBQU+&SHSxp+plmvAEbxDyM%YPm!1Uun5p}zW%n14T)3x7f1$X{hYuRruV2IYM9&+G22{3G*A;pSvba@%(f0NsH7_ilfR2d? zc!rktde7^Ee-EYo=nSRs)Cl*C%lD#3s)f&^CiT1Z*U+3brLoqf9?+Zh(W_%Oqedde zv_2^%9Ogi}E6di;+aZrZIbR_zkS8QuhE&-+q}f&K{T}16I@KkbnjY7G%2E`-e;*Z& z0zEvVHbHL9EWdgRxH$e)lhdPybT=~DAo7zq0-tFxTTEF2?&j_%8f zF`}_+bs@0yzu8`;HQW>{8as+UZVl?2d3#T^=xl(;rC;$<^s*I`px?zL4<6a%dT zxxSvbzMusJ_Y&;lft!jOG~OUf)>&gVoT@!H_}T%-wAkQXxf0@X$7lK(lLm($NlKwy z1UurYK2P__s~01{IeOe%mA#F>o?srgJ${b?Rs+vST4N*I*0wyIcrgP{X3u;G>9_O3 zUW7nB>>dNemMV{l??ij(Z9=58*-*Y+X}Y}?bO(FmFIS<{^|8MxvU>AZBnM9uV8*PNUd4pj4DRI zew0rpPo&P)iZQf}2AWmuKz|-WQ$`M)5HCNaSgNIiuHD0@71(A_;)zk`fy0bafv)Rg$PY73PL>cSO zm=0>q?DGyR5haQUQ^#0p+Pb4Y!tcO%tmJDi`rG6tZAlYH6{aXZlqJ&R3UiG1riHNv z`YaNWQpf2bU#En}r3F_tB_KsS@I6KtXV+^Y$AJ5F^?~T}vkYeXVF$^QaJKL!tQyk& zdH0nR;?sU(lt+BmsE4yd94Yt8n(KYJG&t2b>?AZ+%4eD3_6RL^WGH9n?>DfTzy74E z5a4>E2_L7boksJpypqT^fK@3rh9!LJoC94_V`SAb52ca0ZO(OPwp?ry{ni~`DFvtk zr##F(dqKxGMCvZ4UB+7RYGGqrWM}idh=d

l|`mBx_E0wp;cUFnk){KTa9Cl6VQ5 z6`3qh`goE-#gWqOpZ2jBK?HIk*4*YU3XjZVovAa?>HThV#>Zkl)j3kQVl0ll#!inF z*2ej}j&hY;bJtPwgHc|5_5MPUH~pz8?Dc@78BFIR}Ey z6a|LOYKNqcAq6|b^RcGAF#C*ww-G(t7UwTT)8N8%#CExI;5<|kVJI-UxF~WyKBWa4 zO)Dn^6Q@mroW^0{#B;v5_+T%kcy=C4^Icu5+~Ne2H@#>uR~6Dv5j-NRj7MeygVfeT z4?=YMRM|eaH-YyNyT46UMa4dUBUeZr0eWe^rpah?$O)Cq0B zSGAe!OQm~WOgGrWMH@K14-;uh7&kTuPY$|~f2;B?GZCtNmp0!Y-{7Grhx@3mi{~~U ztt~CG#O6WDxhB5M`hLzu#koTcB)Cx5DURKeNofHD{@fFUM+Z&_WrWh77=7rJcX%TE z?uQ?TBYYv$$+i<7zqS@SErYHaJW_i0N_nXi$!1%K0OSZ}SAaL9%)Pf3A67&sfWe{V zCuuy%C!*WRO{uko05WC$)tI*~u1y%pSGlV=9>#b;Cx+J_wqin|O=-*Z#2y_I8hKB>qU_lD!`4-- zQ(w%*c+MsjV*kw^5y-S0Mw9U}P97Y0(H(o8^q`|o4}-65kLcBQqiMjLfb;Jw2?Q2S zv%vzlx+17l_N|D`{I7j2lXbUt`cX(;f;&JwJm3i035ZTbN)dm0YOfh_pDhW%>mJ%f z{J{-fWD5rz(kH)>cegFXlYHTRUVW`6KTmKeqN3TPn?Sbj=aJ$HD)+z>H!%g zcTNCD;K;J_+di@UvX5non}fbC&iq<5pXATqk&*10xq&^E(hJ0zjhAJ!k$f1osp?EF zGr=(@=85?;(yl1iH0Xtu0k+Cb2aFrax{fC9nMACaGuH&Dr>^ZO;7lzNpU%&KitoB7 zT@NuiJyd<(BXK8E#Ys)B-h&OV#2OS?!j4uW@Cjl)Qd9}fXWahD?5lpjYqU@;ACWCZ zh~%-D0Cv*kbPqcOc(m97JbRo=T}rLD9i;Y3a(yo@-i$c9vD1T*(*LGSLsZJi2lPSp zB{Qq`QE+ts9Dqgnk1a3}C>gLR(*+dQo-?(Fe0nP<1}(3TMTvni+o+Z zFz&D7wDG-h#%2E^z5g=Hx9(A`?vWn=s??Od8CVRI|JTW^?JTjo`!qiczsjDDtm4ZS zZmQOLMw zecpQvxcZ)3+A4aiw<@MV)X@2>$OHW*weBH**ws5P7wZ{&eX*ujhtJGp2PX*!Z;!Cvn;o&!7(CjhAO&j0Fkn$YP znRWUfEvSxEg$hNR@fqU$$z^K>w&Lr|=me$jyc4G1afR=j(TT%AwmX^3%wI1Wh!7&L z;;woJbRul%UsakMnYWwGgVTp#abA(m*Xu~V)`;K1=wzej>+#2H)miI3aH)ep@%$>T zIh-E>`DcGgz3G$O`Iql)` zJSgG04X{pq@VJybE|ZWdpiAHbj0T~#%fOb_Q0*;OZgM3zpmEIcv7zx6NC->7(O#bNEvAJ=d(xTUFx2(FMU915Dvovg|$Hi}>PJKW;bJtV28P)lawDe_ASU=u{|cWaD17l)FI`rV5_Ot9F-OO|4d!Pm3mE9`LVL(-S4-8md_ zYhQXHIii1;V3l0gWO6<0Z^}GrDW$;@r3=G!g?)m)7W4;D}-a-RV`9xK3Uj`3>|QE_%SpkorMkh$Sf$0kNr zU?HIy>-$5-u`*snRo;91;i)8t)&I@k5f zepjf`=eJ!w9s6v&L$j%sf(sJ0$DeVd8H3UG+{Pdwa_fj3p<%7pt8d`v__w!rYfr{W z!H4V4-YgN^nW9cZReRz1mmaPHqa(YhbfjFIjY=e7pI1>bxfYeDLhjwVin;BTG_mil z8&z9ZIw8CH(w%QlWld+)I|c9*=X`g(>1wYT>2o!CVq8F>W&@ZRz6)gbNX9oNM>O_c z$sb>RlyL&T3XuoMzyL$LEGu)Sq#Qt*=AiVPFsj-gz5x0(%_opycB?`SCR6z~5vax_ zh`WeaT>gvVntI{i!{)|kSy15RX78svf|Cdt^zo7AgjO|8`VcX4T) zWx|BiY=HK|RSgu^>8na;?h{v4h|kFr$_2fy)oY7*+_ONXF{C$tf& z>(n(sSH!!h4*5&>WwEl9U3K=FP1jPg-^G;mxu{xtOWXVaQDn)=<{O;5utMhlBt?Ta zUnz|kD;)zBF};wZiGj0)ovpBevk5V!Fc%X86B7d~10w?m3p*1h4FeN^fdTLzCu3*) z|3(rmEyYp)%Oa*!Hc=;*ws18e{$EDoprrvQ3)BBRh~<^$hV6zps?UqsV__4Vl26aC zKoD<B0w_^KbkKTA`9jAU5QI`u6`9V`>M0m-(ozVc6Z5PvfRqU9oa6e8VHTwj zkok|T?9yJrUdmkq5C;M1Pz+UpLq7T;15^WdjE6LQ+KeXhg3v8Y_7wm8R7}xB$&zcW zStQXAStP-ZShiu{{S}GG8nQG%O7~(_wwWu^SrzyCD-T-hCL#TC9FDiAe`ZnGD4@7TcG3HnN}Cvt-0 zM3jmP>*BNb4VD4$j?$r4%9@fhVxz5w%Ng%Dot)e}&CQ~>peJ`hl0l4#qYpCOqydes z?)d?Z_na9(AT>S3oU{|#RoNCS9_MK%uk7|7v>C7eUzqYppvl*taXp|3(!7Y$0n+SJ z)J_T9QlcSWJ}WpBLloF0ooax{NyAtkwkeA&gQmgzvxV`?+6r|hyvB_aSB?p-t`XFe zPSVgWbwyr-m&0?G!p9Erw_DYNkTWku3Y*K9%Ki)+^6lVH57y5Q*8b1n57e;U6$VhK z;Xt(}sK>$*__12Pdo})&XEc%K(_43b1m-kAP~MGYidX(T4bQ}wbztTI7T*=8ko*A9 z{~YosLA7XYlQo5!MhPsILI0WKD zDeP+ua&i$h@?s!NePjvK!HweHdDuEd(KoLyvLmBSXo<1L7sq%k`~J?Jvv3ZX!@pY zNu=B{3P4o!n*5c<1#Ny-QyY=RGhrIYl&dPDvC|`CH|zBIet0+)3hd74mZ+c?OI#u$Hv-k#D8Z1 zw^CKOrlCd>=QsvXoomW3kJ*n2KpU_Nn=1eC&5We?YoDud`*?^}7*A3srlJLwyp>XK zE0XGw>8_`D(1$YQs_n$+5?houRHp1Oo~>^fz$2}M zG|_gptz3&bPl8tWEWCMk{Ms>9uTD(_&WM2H4Iej@e-0zYh7Ofh4z%Bl8>r4_A!Ty9 zjTW9cXKl$tyLYwyqKcvP7qfnUJ_`nKW}Ns}Za%)g`Ej*i6=90LJ8QJ8IE~<6{<|E( zI0W&H#6N{_!QJ(OG(S?60vl_?Ck`QAugQF`Zj3;1Q4iQZWMZdYA-ts#6!!* z1o3uq0i#M5F!Bwt&|=pl0@!Hza*)@aT-@xB_xSRE-F|<`?M1j#s#R(qL}0`YB@-le zPhnKpISrK)9gkNJ>Bhz!{ZZ?m*_A8`0zXVfth-#uY}+m_P;~JR{HwLuQE}(@BZ~BD=)PXFwknfHZnW1}M=G1IDWZ@Tm-8 z9LcBX;wH9;UoME);jLna;yAGqyF1KqE51?grVt83MMEGh6FkmsJcrE&^&5rbU4lTd@md zLYtmZJGsm=x?OxfFD_`n(L_U@O#$pc7ta5j!TvvE0~@v4v=@S)Ixm!v8r0!4)_#sB z^`JGjoj=xfEo=LeNDU?zziUDV$3m!OdH7V8iImLl{0(A!FSl#%-3jwDWb9?$w>oi8 z(BON~>^Lh}h2=QuYS8tXlP784(Dm-b;jvA&e_l|4&|{x_8jKwM4-y(K zr$i)V4r#u!4@^?Rq2C)QT6_q@LuJ_L>{mQ4H=GpF+69Uw^Cq4{&-grkEH zyC55fFe9@7i!c+bpb#sIkcfb&C=06)DS8LIMF zRU-a&EwOCpym1qs-taLRpe&<^;KGsscT$H{?CLl-C#4wsjlr7=IaYjf>XfkGM%(_??V^W#tPoZgE7)T0VdpsSw`DbDv*WC#$bM^jIhVbPm za%Q!Kv43?ToX01bUaRiL5a}aFXRN{Q?HI^E$SBL$mu^RN6pHl);#)yDo*3y&2+PdO N0!vOVA}0#_e*k#smVN*L delta 13172 zcmai)LwKMKu%%1uj zPeJPnu<{nHON3*nF~k5Pfza?|a+G zR}g5o!WxoZAmbLIeh(r);2WpZ?j8D2P3PN`G`tZc z1K@p?y`!DY8;$ED&@PD2ZJT{m6OGJp77=ni$05IBoq5j^Dd}@RQMTpwerU*Uaa8h7 zP0=W{_>8PF@E4r&`?S9|=hof_fH-)3xs6gezB`->e=ubG_s$?0=Wm2<$FL5l1bZzz#q zGR)h^OiE8tWw~H+By569kGp${P#e1(3P{fTIIBjtqkM6FcYBc05f?^PEKUnX{wy1J zUVR-%f8Txf@tVQBT2aA;jp(lPF^(7|;)Vyflx>`wR>O8Ul z{N%nwt$cJktisdc>kyXU`|_Xfuj{jy;j~vm!`@0#AR)UZWQtb^q_LReZ=&#QLW!UG z_NrZhCYy=mJDcwev1@cc8F?aNVP?%D3yA>mbV%_u`a)fXSt_s-yS7FI%P>=1I%|n- z>h(gpHT>ulE*kYJL-8M=f`4%&k7W~dP%=E$6HRDF%CY6xug2hs+y!sLPZ3j=`CI2+NjHkZRcj;%N-c)?kr9C zFI=`lrc0!5%Q6BxI?-7hf_Sj>x^u@wi81!fIafyEs2-SoOP7sL1;4m-EgJ~LCIXA{ z(xqAqi@R0IvV%x0e^C|bv?vUAss;f>6U%DBZqx)qx4hzJC~{uOT{S=v)h3Z9?bAWZ;7K#1T|t3aOE&?$B`r`<2Yjfaz@+~lp&d0u44abq6j z+|bf|C%Vd2`bx1J$8_7A!}4^u^gAMt4pp9S&j|FyQ24)+*l#79<0q9}$ALk@2qWk? z5WANL6tye;5IOmY>i3LV30^^$Ah4GUtTqKcBtEijmRBbb*b-~)6@vi8p^HT3F_CIn zHNsf6V;9z}nIYH~l@J_nl_6>%CFR&5Cpcv%o75ZNc1m zh|*VHMDPBTLMrh9``TTS+t#0#iD(jiJmuYsS7L_Bc~-ok&FK0b*3ZG!tbd9*u&e*n z8_KT0S`MfG`D8?MgI)pPyt6hfGqxhCQgtwDMI8KtD7nZfOKAI)XYuaWwYZ%e;o!^z62%?F0FZ2t=}fKY-Mm~FCqCQV267TXG8 zZq{<~-z1Eq@X9djD8!C79~9@vK;MI!3ZvkgooOw>MGwsU`#}ca!L^o$2o2exIPxpJ z^qMbY+~JH11ThaR^^XQK8`>0(N)d3i$>Gg!$SoYGH5rZtnE}~PK9NPxA3VhWa2>}J zYE|-2hF^j^NWJho6L*>I#VGxal^Tj1Iv?|xBqt|*Dv>mhG0Ez4mvZBVR`)N#4ins> z+E~u22#Jo*=D>ibH>T-(71<`LQDq)RPu!zby|txaXuQIJJl9y4N#XjURBO=SF764jTa7y{#Y zF5lnb%r9*&5WY9qE|iT*7PKtohbWrv6&}z3MjAqk|1tr=`Lbep-}FCuTv3yEd0BpD zmycyUMIX18o`JaUv-0FVY2n&RY3-){5>LMGLVoy7R==WY`gbj3v8hnwZ9YUZ+W}zK z-9B`|%{83$TX`~VrlDL>j`&hKUQ!NOJc{xf>+3+a<{DKt&MULz@-1}^O481fgW=c* zR^^-$;f(-GH5u=}b(seg4x&#*>1TQgDZfZ@;&b@9gB^R;6?8-}1!mWDrXm)U#1BJa7i`2lQ@_sLbIa@#^9(p3orNCZ6j>>1zVe3$M$PNjtqp_&e-e})vMv% za3dJj8KSIyYOFc2+15F2%TG^~2xcdjb9L_<79bO)E5>W*-Qy)8D{m0Z){|8rM8_da#)?xA&REp{4t z$PNJ7%g)n!TFcZQbRpsH5be%8_xACeFxekT}VouGN7!YOZmxGMum zc$sH~8yt&BrvFr>3BM7SC%f-&7Ap?6G~b`j_hxAfcMNp1NWcdrS9CNNmo^RHj)~Q& z4$E8{c?O+R975hg0?%A?qc+@)w)EDao6#7-|>gHpB)@UC9*FgOw83-5c$$z{W+g(|{FJ?T7uzWFuhzpsRtU{?BFktpdFcEjz9>S6aBO_b+n6StRf5 zf9Rs7O*k_}ZspzMc#(|MPCwWoi~`ZN&YkLT8aQUMIf`92nK(GN#>MHSHu#xX4o*2Y zqp_?h=UATPG^p71#3CYU@RRXjEFUkO*|Ij8EAjR8 z;LBrh=xk>XVN56g`iXNsN}FwBr}8mu|B0BnP$|o9Tv3&39cn1IDSDKMviEeHnkWAb zoO#7Y9o;N~3Uc09L1^u9;sk&Tagx3&x{bfd?0zB6#=CN>2hABeRw4`566!ZvL?cmO z+J_h2SM_O>v_WsC@>}txSV` zQmaw!fbsDz=euNQmTQEsMiYy_p;12k!ULL+(AM;%8Zzm~Zs!-FM_R_N(>wHeiDr|76YyoP@vIjBmRn&hADN$a6 zrCcdLKHaa|hASgiqSqumBkPCZ?M^NDh;{IScfC1eoXZw0xaNQg!!LJvZ?X9~Jzj%aWzHQGg*OL7#aMbe2ohSk7q)ebj~1t1T5{a?WDR%L8W2 zn5Mcz?9ssZ8$zPTUV$eSb)j!)cgEa?VXnr@afJc6eT-@?D30&(L;YFvrS)ae<86d? z5aSY+n6{FB|25Durpod&I&RvXV*+UyDu^8kcksRkUz`3NO4#zJA^UxIKWh)fgnKrZ z5zvQb59Z)b1>mD>UE?KfN{Z&A)4t{=HS!AR%le}W3uqA#azGWT^ER^ zhDxWTfmJyTym{_80h}Ka?>2d!pM-+FOdOT*yUQ&;HQSMkml;{J?D%T8v}lZ7IuSvn zxqp|zG60idr*oxEyRCU!?-%j&?v zs9sodahffsi2dxu+N?bf^P6w_p@7||A8%JYN`@o*jdScstf+Mx*4qoi026w3d=!=;S z{}L#?Tn;X*^33o$U%|5frv?kR?V0}Vp9NAbQAW^lXo%Xcy)y!L1?66frg$2w@hoeNQ@tg^yKm=HAPzS$5wPr1MD@c6mweeZt!>+`n->d zjsVRixbGFXKI8N5fWVg-<56(}k=U%8qv(@yFwpk^t#;+meWCUvGSf0vWVoG$4qdA7njdc}WX|@s zfLFJ5rPvNc=EH{c+OEom$;N!LuwTS0#}KB5ZjH;x0H(64d^E~&U@O_VL4&4p13KT8 zNlWz3vP+W)7SPCCc@I`CWRvVGOLv-GJ4BXyuiD_v-I>qVX|>(eSzu;~dj8Xt6N{;~ ztC0lw#?l1m%5KcWGDU>-n7)AqvFCw!O@t*^0ssA*@&B16#agf)Dyj`vCG7`CKUjp; z{bGcUBS<4%0*Q(HVVWdEo5-@`AdEDUK$cCHCCeAa^dq-@=c|^v9nc?7T+_! zJ2qmj=Wna&vj$yN%ehKFV?HqlJy&pz9NP)zL0q~5;t?lok?T8H?h zs&{p4Of5^9yQ_qf5o1pe%rK%24C*q;T?wTM4UxC>rSeT01PL!A@mKjw{Xz6^J;C&E zk8EL%YNfw0!fqiO*2$lmps$P?RyTXi-?uboW8-pYy@P1ybyj;wD#d@?3I^CDX6bF5 zyRVT0u_pum^ONC54cbmnSd>s$*n><7Beb1aM%!sUOoGPw-IGyMhbeOsDJnZO%wcM! z*}P4d9=Zk1vou&5jc{a4{);rjc;ew|+Xg?EkDZaP7DlY^N9}Td57S}|w()TKChVg@ z3Wk04exriDD9d0n@vSD%Q)C#+rm!w_-was*_1gkWdgFI5)j0_QTHpFef09%ZnNE{M z(B?_PIq9RcT}+|de8R-*DWO)RO)lPb3YICk8Tt9hMh>a#u*TdZ>!kmT7Oel=rD!s8 z#vt~kk6on1k}_gvIeconBg>qzhDp2W+@$}-cSLuybQJGUJwYw8y81!_GGx`bMjmPd zz?+l^xE;OJd)+P_IdOc*tx`&F87$2bYcYu6r%|h!U6k(_DVliK)uEX6P;n0x=&YvT z-5g^OEd7w_I++^EyXf2CPDAbLOSY>VITpEcHg&Jl(hd8!kBClohn5>=8YsGt2r;V` zEjSSdh4_9O09t;xZtAw{uzG02c_JwQ#A1hwPv5<-&_n1bkZ9Gj>Q3W7G2qg{#$CF+ ziquwuNH+!Zx_A@^3XS2BlED1jne;cXg**webx8?ZL3A>VbHQZoY1Pa|ki&G70tF}G zY#{3-s3jB#XnSkp5w!2i5O>~M%7LGYR5{l24N%Wfc!!fCTUifD`7<@k2Ser$aEhRi zzF&FQ3XZyB7`}Rd8Kk2Qp2x$Hoo^zU6M|Et_>$X&V~B@65MvQqCg?v&1e^`rwP(Wk zm<_qKj1Tf&+PnX>I+{Fl!%Bi_WB;2wafGY^`;XN5+VtPsT3siY6{+_XB1k34G`f9D z+QQUW3TytluhSwTlZo*uBkN=opbp0>(W2x3wO)X5q;8X_`V;h?*wf3)`xDbmEDzD$ ztIh^rO`cCW7t4D*W#S|be25ML9-N@#gD?}_#o{kl98=%VS2!~gbf>&e#w0sr`1@`q z#*{$n=MHl1vXY=_QR^0lvf;pLTRx9D2Vy2{_{N;5SkuzxJk>SAgHUQ{U>pLCx9HUG zaAerMGfOEiq^rMs@tqhj!UHDFm8|bSLuQ~mh654?sx&VHa_-s@URnh1cB2IiK6ht? z5bs`B!I`)^RB1JIAs~kTkb)CIpRsYHE8v~%pzR96Ax!4eEuT#qiq-oOEEyE<8kZzg zV|ei6Aaw2|MTm@PQhDnDa>GpUODE5V9X!aPCqp8{)EWbJe>S34}zsX=5~R|lJPt{50l3%6V_ z)0$ix2%fAsc4`GUMZsa= zpFW@H3hXOB1r}DRu3Q*}$(Qi)ZJ^l>y@vb##CX?Qq+h zeGyGgRjh(HEkCKzGHmu@*JrAEe{3Vqz3iSf&AHHZcmm!=J@kto58lDmHAz{D4|!l!5sl{omP8EIg6 zQ)V_=)-wzg0G}Z{`PB_Z31$xCMzyw$ax*)M5!B%}v-bWLM{rOVBwQN$mzvCj#-&Xo zQd+KaBB-lgtZ`p)fD(GxBK(HEX&^bc&J>dGyN=c(7 zDvLTRNfoT3o1;vntPIXMnoYpmVr-a8ni0JuOrBb>@^aR(nT*@?``&^Xh0Ffc-lshh zarP<^jQU-woi^pcYK5*GRepN3G8aCq!er_KSV=Ma*|BQv%~lQBgv*OEl#nHo>k6pU zk5Q+WAECmYLTx0)AR`)iRWMB_naB`W8o(qn9jGwXkwGaIAkMK44`NF&Qcy&^s97}r zq#&al-aS*73EK)IA`5ar@%85q!Zw#-j$tg`Y@SGgBt^Mm{>vW4s3}uEEE1HKVids! zG{P56XIVwaB0KzXF}?{04fZIJV2Q?!Ms~_cZ%&-V+ z+OPpn6T2A9mzOZYrx&S*c~fTtS!4DiP*N-M2k2Mnl2YI;h*0^Idn~I+tZ0;~^pYu7 z=FRs~GFA31;Hpkxo6105+lKw-`pCSI-c22_|3ka$-v7<=LA3jg@XZi_)ek9nLL~wd zYoTIgRv%gc{eC!CS)sJ3w%B@x?VA3k)Y;^AZ6PAte&q44c&XkBw0>gHN1YD=-GiKM zT36jjx?HRwmi<|VL^oP~+8(72C@TFfyE-Gw+=MZ8qB_1sFP0W+epYJxGyJU9dEH8W zl*Pqe!p;-=E_o{P`7W^HqFw^xAqnJtotfkETux|IovR;SJCIE(j`2;q4>(hnO2yzA zUV$YEgsdbPE(G$-0SHjcCJd55hiJz<{}<8K&f^A|7mLhp#i zCK2R&nhDxtx||jRTp38^{yY+XB1>vpl`GbYSe>8nwH7gP_grrW>=}Q6zf;=b(H}WH z+2X_Vsg{A+X7hG$w6Xdb@?8h+MJx)}d7$?vWN$EwYADyHzD30adY1$67TRyekXMCNIBUWsPnQrt%{F#M5)|`RSXPQzZ zSH7Nrs*j^b>$S`gV3CgSM)vAmAP4;J1OPdO{2g+M*AlqAWoHNQbiv0AOr<_`!IU%R zucQnei`C{%*xGJ&U6bJlK2r)YKa|9x4`SU_-g9s?*k$T@-=kT`X|OgK8655O5D(0f zqt(>Mu_tcjQd5u4pH5_KniSZz$5w%3PxsaR#_Zuqb&uQ690*~U%ml}JX*2}U?{8`U zC}%9+fB^9+{xJ;nX_e{z8%2I_{NZWg|;o*H_ec#MXDeVC;2LrOVL&U`kcwD=|XY zQ8yh1>j}%z)f#4Fx6ys2zv=Zc@?+;BtuaSGG`#El;;jPQTH@^aNE*-oi34Pf4AwCT zzg?Twv63if;>`Iv1rXFnwn}18^+U<@TdGqYzTZ{v`bT^W2~zbk^mvv8T>*TlW`V+2 zB54-|{Z+=^9>e{sXKSRINm&%vew^ ztdVIXOt^DqG2Oaz+n{J0^-9tq6FR;ZVboh(vdfQcVDDaZ*<+}Zmd0)59jcP1tOXf8 z)IWO$J86dAQm$}$eY~QJMtqEpzIx;F{UUSsQz4sUPrRBsixjC;uE@}?;EKDt48n?! zlm{*s*d$GUrTb@d8@{`7A=Tb!TNN0edT^ygO{7Rr5R8Z-y(xG~`O2JDaEf6Pqb@_m zxrz8*(tN2r_KGbw>3)By6vq~kUfpyqvRvPAIU(hs_6g&YWjs-IPw)`A7n%n|>d1Ud zogs(u2a_jI5PoJJSzvL=K+}1aYD2}1(E)Q!kp+!Z$$1Y@#UqBM)Tb3L1;unBD=Ap{ zqGEPG#^5#{l4D$KPhHwfshb}BQ?^o4q}GZ>#VKg#N|QnJ4gyF|hWxep;6O;t zSwS6g2NE_Pu>0E;6~)bLl?fS?Y6U(gLm^!^(*A5oX$;s?T!uqF6xD&V&Z<+01^~?_ zl6RRt?V(+;_vdX<6_SzWm#LDD5%YxWKc8jaY$qsnzS0Ud;+;K||t1Zc(8=jp6T zXTwJf8#UYV8Lr-v@|ebSCg$RG`gT|~_mK}ifk>pKd`0Ok4k;!O zM$X&TbSk&v_BeE%bh>R#p8z~^aqZ2J;K)g#9#JU?MUl+S?l!?3a>vWf0io>#ei)(u zIOgAp)y@}OG=PjhY+JSm@F54QAF?Qw8F7;8b{ifXRf@@}KmgP?6|2_s?|Gr;X zcI1qS*W3>vx?J~75Xt@-tH+~s_$<;_<@qvXU$diTS6&n3>J#Mq2m!oB1U%*6zKwpd z$Rz+5Khv$DaVdk*X>WD5T~I&nTX?y7Q~mwOF0lY$SCOO%LAqy-fe8@^jlIg zxr}Y(sBfIdvFIvEvy+L4t<-qc6;kwUvZiNfk7BB81ZH{?t`_DuRC`{@(+bT`lpkVU zjQ+ji65#83c3j=8bpzMFp7f^WU=TDru% z=U}W#7*1-x3$)!letVvA{p$-+8vWDLWE@it!HYj|Q=9#EQwwDCe|FqCtzjLNjv$ksW0ec#oae*z>rb-!sB2k3 zvU7?oBp>pZfm4UaWvz%fv+EZ|PqcmQ_DzdkWtXbj_586nW&YM2qRXS=A@@-Rx}H=| zaksAIglk>1M-bqLWuw({spL8!M^e>2G+=q>>pOLUkyr?~lg^PEDegjBfo!J@`;j2( zTq1Y2zzkI|uJp;yO+uH+Z_8BMElIJNzJBzqSE|UuN6znqGx?-l+yT#~W9m8;D~+di zrP<@Dtvqn^n6h^JSh$p2BUm6uq|=>~t2Z!}6@N+hhZ#s~Hu19U3+RfRzGl$%1ip5q zdcK71rtij7`8-f9e!p2=X?(R9WophGrkVy<>>M=Q?NN=M&nczI5{b7g&%9*mtd@VB z1e)dE1z+hvhn40^ztWaeMXVwA`YqN)=e9&->SVCiz?cnWN*j>>yQaKP?Hc$dsBq&$ z+(>w~?gg~h{?2F&Po>>!O($`7<+{a)dir!Ggopq1fpv-rtnSv9`*d@9XW{u;Nh%|608)oVpKd4(Wch zT8^)!$ALHb0$h3K9S9iOOg(sbk{+L~e4fY|8lUX3bee|QETxTJs zc|!d!{feYMq{FI=iU+vINEDqvB%#C}4=omHo4r$U<#SNjKU3^Z?NT6@Zb4 zLdC$jh1`AK2AfCSa$Az~iges&EG|bG%co)SwXyif^1S;ebn)UTTZcGwu&JFn?P=vz zeo9 zjm}fSgE7}l>sNC=@D=$tGyD3%mrdri(#|P5p(!Lvx5Hwp1d`w+LevnRG?+l>v;R+I z3PVKLOUJ%9Ug|HMwl=OFZU!uzUMb63 z@(+oi3~Sk$DK2YGX#g7MSYRvBdZ>X)z97xnbMCtRMCe#-Y`^ZE8MNJv#2BT^ z6fvzs<8p&51=^Cz0IbM2)Zc*ExvO-a(Gr?G$_1MN_JS)Sl{+z&k${0TSAI*#P^}eo z-cXs=n-SpiRq2D~tApXvdKGBTb-<1(b}6q}UHVi!{9=eM!*0hTEg7v>xRdHSMg;w$CP{CBqZ&@0`%MUol6@FqtT9#y3lP9)h1 z{^gd297({=|DYB&3IU5~61$6YBHNA=j|U?|rWU!2Cn*A<7K4k=i6bF%Im&M|_!B%0 zW(H6V(<7WS>mDl;b=S?J40mzN9e7hPLZ*J!yx2v;TQbi)>}( zWUl7jZK>FT_tghDp^U0VBOzZ0Eg1_vGc_@Tu#>5wi>1Ath@p!qF_j1xGb1xIBP$Cd z69*e76Jz3sB`)m$Y(!QPKmI!-rcyE0AeOOoGbR2{&XnkBWeCQ?@&6mATAKFj94LM> zwL8XLk)vJ62K55-O_p=CvJIt~(2HuipfRSScLkr%?}(;j?tARib>bkIMWgAvareGO zqHB!PJS;-YeYf!$igQ#G!R86pWPy_Vh{B0Kl$cM`8YmcX(ozVM6D-Le0+eK|Dbwa< z@a)o@WVG$l??w^NIPU<1{K2LLFsV`A9K;2^T^!NtH~|I;NBjcd z*ul+{P@t3?&S0btFA~;BjB=&BOe)#J{4|VMJDeZS8+~midi{Xrahkf0;ZdA6mFE!~ z1tiHuEz77GS}#cuv+S>(&A#OWC*BRE_z`>S60zyl&gGW@138Uqg$Yn zW8#tV(mw1T6l$z_{X`E%q!QOpCHQ>{Z+5)r$}a2?yNuA4*fra__@F6SUe8Fz!;83sup8vKGD^FRB4!Lb+Hq=*uGiqW@L zvhn@FIXN1->Y0f^mIZTRMZoshbgp-jX5}I$m(N(`n?LN^_TGm`8#%n#Rr@>nrI8JS z=kEJ^=o=9FAbJI6UMjoy>@8e2&Wdk-tJ>meV{ZKNK?Jy3PAOc}1***A>NtPNYt ztge#U@=!XJ;6kMb1;gKAf`T{V#of~fD}_1us$MXB*evjeoc3bEC=rQ z3V-~JMsN?f^z%2~Y}~8xKfZ9t7^)}h5UvirPHueZcs}`nC5I#@m2#3APU=z@Q^-+L zYO!5(S_iyqI1g6~O!ZhaFe|mvEso8a3!CUvvx8ihy)Fb%y zjh!l}m0MD}MoWgOF3gp=;v(2;8wGQ6&~puAz)S)q$+F=s<6i`rxa6hN@>oa`a@`v? z-mig=u_EcDkd%jTw3uk~!nyuJL_>Xe_(TrcCjiY&jiNt;J2+VaA_NZW$Jl^hO0#l! zk`@01+`=9shBvGiqckDWX=4 zes)&Z*ZoLp;y5H#X~%)drW+aR#8o5>!QtorE#Q!32-lIS>UK|ikK~wsZb5fWn0r_#WBBW_ zir3Ros?lVUIT{N*sCYG$hEIt+x3;5+&Rrj2)>qG$(<=spJKL=JBSvs}3rXoge|CJK zP}%0}M^G1yAI`BO-R~>8-#d(plilr&+s!9woLWHPz@r;jj|`J8!!S`K4ExE^0#NbM zj}!|%6k0XVVLu_LHlK!^$>cs-IA)TxsQ}~A-3US*gB|c}{ie5I3-QD_QC?;-y0-D! zUBVq92JdjfWNq1p7!W~{f%q@FZw~_Y-$UAPr#}p8Jm~sv2wsT{YW8e{m(nnMSmbJl98Bt zODfy9y2{EdFa*`ab#R5WMT&3v{Ay3#;A6w;6kWzJNg$$0B(cazMRduMDFCJR6;P{g zHJA7$8th+^aM-ghKP6IKEEaB;V<_(|#W%xY9;pc5XA9U{`6uOTrgM5ZhbHw)_D=~I zThpRRA&+3eO9Pdqi7D6UgYYK?!49M{bcs_t1+UZvuL$7|xI?;Nokm*yd3;z#-DMwf zM{U8Ktb5=`U3KtbB~X8<4FUu|n?$KGhj2d~Ib*Gx<{V99-~ELpK)lglQ5W}}Vx}@v zpx5K_YpNY9PFuO_B9cjj)-qENt3vOE+rJpp zjpADF9qnnW|2eFN?-%35`>b{skPAX^d}s0lrg?l{&n`Aq(MA)ESb-Hm>>y9h{%ga% zauY*S^*Zcly5M?m)DQ-=;Zux$jz@*yRrW19oBB)}$D_>E2G<02;XM;!3`)Wrn#$|) zg_n6oVQ#nUR8Jlhg(-?Ql213a=sPC#n{jP9+P6ZXhfCFthuJhM)_XWXwfkHA1%AOJ z2J+kPrRpkQ2%)pD8=&cgXqTY4it8a2C4obRzr-`0yg(SZ3S%RBD>Tx0h|H8so|3Yf zbFz-SnEel1n#+(rlTEZEuV(eIwJFlb8fvWcGg%^ujAE^-W8Sn<3-$W72rlsImBdvm zbW`;Ye|t9bVNDc7whq|92_FBxeIbLKi7-Svdd2A{iMk)lC6e#7CS{q_1K-=!FIgqo zv!`5rY2(XMru+PYBKNfXooHx@mYC|KCnm`FoAEcRATt}M7$Z9yqmYOY6SFXz2s5)7 zo0y=GFe4u^&;KsbO%#A6Ow@G71-Rve6tM?y)8Tb;9Teke0~sK;XU2!?pbNX*#L)1x zQw??e!~aw|fMeQ$Sf@IE0GPd#CU=MUb4R&7$MTXqt&9E!(6l=CSb@?C%BGqp2ucKPo)vi-l4y^$51vx}jVi-(h`85}bw PD3a^pd diff --git a/2nd/18_Vecteur_et_coordonnées/4B_determinant_colinearite.tex b/2nd/18_Vecteur_et_coordonnées/4B_determinant_colinearite.tex index f70a0e7..0207297 100644 --- a/2nd/18_Vecteur_et_coordonnées/4B_determinant_colinearite.tex +++ b/2nd/18_Vecteur_et_coordonnées/4B_determinant_colinearite.tex @@ -21,7 +21,7 @@ S'il existe un nombre $k$ tel que $\vect{u} = k \vect{v}$ on dira alors que $\vect{u}$ et $\vect{v}$ sont \textbf{colinéaires}. \begin{center} - \begin{tikzpicture} + \begin{tikzpicture}[scale=0.7] \repereOIJ{-1}{5}{-1}{5} \draw [->, very thick] (1, 2) -- node [midway, above] {$\vect{u}$} (3, 3); \draw [->, very thick] (1, 1) -- node [midway, above] {$\vect{v}$} (5, 3); @@ -42,7 +42,7 @@ \end{itemize} \begin{definition}[ Déterminant ] - On appelle \textbf{déterminant} des vecteurs $\vect{u}\; \vectCoord{x_u}{y_u}$ et $vect{v}\; \vectCoord{x_v}{y_v}$ le nombre + On appelle \textbf{déterminant} des vecteurs $\vect{u}\; \vectCoord{x_u}{y_u}$ et $\vect{v}\; \vectCoord{x_v}{y_v}$ le nombre \[ det(\vect{u}, \vect{v}) = x_u\times y_v - x_v\times y_u \] diff --git a/2nd/18_Vecteur_et_coordonnées/4E_determinant_colinearite.pdf b/2nd/18_Vecteur_et_coordonnées/4E_determinant_colinearite.pdf new file mode 100644 index 0000000000000000000000000000000000000000..2afec1e266bfc228df3fa73a6ee5f301eb01d187 GIT binary patch literal 24790 zcmced1CS-%)~3s5mu=g&ZQHhOv&*(!UAApoUAC?1@Be4!eiL)!#>7P2dm>JrjGcLM z=Zf{_j=i6EC5gPSC=CNG3lz!ZQs3gx>g?b!6f-_OzMY{Z6gM|MowA3$2|k^=oS~(O zkuyG>l8d49f3=9(IojaU{k8qCGZ^sc1O@Hf@wNW^l^&mg{=dIE_;fM`&W;v;wKM$p zk^kEMX;(CHvU71XGI7FZ`O~EM=Ta8d&L)n3eyt6hO@vL1?2P~PD{W$H=4_77z=F@q zi~qkqP)^Q{CI&W8?&}Ni)AHogyFdWopMW<|Cbq`^^T?mQzwV#y&z1jkaj^f};^6p? z#=-Dc2LC+?Vfae~|GA7XF#h`@`Oj*L;om1N#=p}2pUVm3UlREDsEd*5KO4zk!{omy z64w80B!7wd-xCSb-*fV>hImGHdggx&^8Xm(m$b%W4_XnsR@6?wBd7H3K`}v%-BjV| z**09TCM_<~quzJhUYhLm-g&M zIkeN+$>rMW!l{CcY{S^~9M2`8Rndsv3sSIk`e6CKQj>I`iMd-w`Oy?J&=HqDlYZS# zH2kLbGrW;4y*AR~_+;A7ylv`^`A(&OoOObK5c!>-EVnEWKk4U?( zi0|CFsM|F^r42h^ExJZ0_s{D+JVaJ_a}oh-AqFtUc$gT|2WXOW5r1v6m`QwvC=s(8 zoqjj+3QTFN zDYl%M{At|&D;@~p%pndx zB2Ra4R+Lbf?a3;_o#tn!Nkn_MDPu02A)plYWzpmEr_{a(c~w&JTj)Ruta8L+JytKR z3em7jOuki2et1RAmime3rjV--TX>G`wE_A->656dAC_72?Nuy{Ltjq^& z-_Z+|(b;ZL#(-UN(d60&4_QH@JZb~FcZA7g>ui`q-$n4#BLpIbm0nmU7$WwY3&gd7 z?T}t~QZ)=@^PGq}yKyD~182V=kCYM#vqB+mm!w?uY?f1EQFKi4q!G~hJl(<$B|$bs zw@NylmI0pCa#%`2X7|405yM1rJave(Jro0wit1}So_kj4^i`4y>WxP1nVQiI{ z)D34b*ZCaCg8qk-et;6_AZ8u*O_hJ`F1i#|Z)b|41qpTsoPOhQ4(wG;#vKy*e9qBHKiLz9eL){*-sIXF0mgC=jM%JG-EdU$3)`HhKyOr zJfa0EVBcN{7A7IjloErHPZ5o`>J)zXKSM98tr`neCwt|VQp68+OOI);m+@k`jYNj$ zzj-`LB64+79K3=#+7m}LpTYv(6D}W7!W) zyM08f5K?2T=O~$vvLJbLQ zU~Ww~0)ej)(L~x)A1}uziTkM^Wjspp*hjp|NtASSjo)_&p+&sf?;ReE^TV2lBxh|* z#mVV79^%|>TxHFiI0EVjB;u#RtsBbNlK7i+VJpfPRreSWhE<_I?v8W66OTlkt)ZSq zC1#YeGn4qmNsfS^v~H$~==WwF2b1lQQOU&A&XTjHXZV_WEEOYosF3&k4@|5On=%%M z@JWoc0hXh(G3*@4B9>w_Zcn(ot*oclvClVnewV)l+%}WA_<4yaohtb5*geFi%rPz zO9e>tz0wJ={VuS<>uao78)Mz<$0^Jz4-axfQsu)AT8EsX$(b_q;;}3H@ZIW#&!vN< z*JcTS>x&jinNsW|+lYf1WI#TTu_J=P#k|GJLk5#(cyjiHkSId@48YRS8CM)L63678gG|!MArxt#x(EsiD(sblzupXkH?NJzw%+f zH(+mwjfmihJRWrq+=I(o>lOdWbE!#@0DJs^L&ZZhNNm5a(*C(L3m20ujWYo#O=!;! z>C~Fu**DXN{Q%{l?WSMzGuK@eCvAWLGVNEPz!arPelb|4W*5||ZHKbdhnCNCDRxrRpe~ z%(5g-oyIDXjTRaSxu2Oi7Fl+ zLGN+5A4cg-*Q=3rmV}r1I<7fda~&a7=7Ox^-Cb~PSJaUXpb(J_GjSIqjN-VE6dbV^>86H zwVIRmXd0GnbMrE=Ksp25BQoqt3i=Fu1~u)}%Qt2e^sE>;>jheF?!zVPRtf8YL#5hc z!zwsGDY{#d?0;;AM~{W7OzqKqx=ZXrQQ9^u#LV)UB#AzZkrY3ug4i#&{ZXWg(y=Nl zx5B%j_`yByS<`xAmNGU&Bs`4A5Q;oIKA#2!I2J2K$lh9+*h4RP?H=32@yMb!SrM6K zxM!ZlI_r7Jz$PwdyTi8B!#zIy;IK4J!>6UaV}W1S!rt|0O2nccWFTWSNHK^*%{SCB zvwfb;h4)BH%{AFUf7O1NppmS4BjKI^J$q++5`2Uzh8+m`( z0RjU9LlgqSfrWxG6M%zR0&);8Da?qT0sF#%g0Y5y03e=&QvQ>^|Gv=u-}FaFLRi$! z*7+~=Lof8N*$oTxKcCnaYd~r%sV&Pz2aF(DFvK)ixUVm>=oeek#7YI@D?l&{)3`Db z!`~B+MQQN!Q`sgvDkxXItAZv)=B`_6aWOVCsZeRQD4Z(}X;#KA)HY>LZysxN_HaCt zRB`UubzdV5wQPD#e}Bwyd^-V4imcQ?6)UbeIY#zbk7II=Wg0-U@6&ul=S>_H+DZQ) zdlZ=CEKe0Yt4?y(DPm84n5a2Wo2#Ii)A@eYtbH%TnyU1oLgx8}SGZ$kXZ0M{bFqOKF;|~y1#DFcuwm8$&?*<6X2bn z_BP!tCrZxS^hBH|_2L2Y%m2jXPWzWk+Ft!FZ#!wMlwfAlxf0LEQGIS@XsS zkgs~B(oLAEag;}ZU}oI$Zh%zXJucq`tS5G795g@wT8T65!i1M#)PfN7!zS|fF`6(u z8?%AA;HbJg9g7iK7ZCc`p^jmGPJ;*bL;lnu8i!VZjQyIU4mX)mlS6qZ8oL&LgbNtZ zb`gQlhimRG>#`G`ikMB=-s{I+pjJ8GThGZ!=60E7U;isE6cUlLK z)bZoDKvun7XATvVbaUAgTfjd&*Mw)!QSx8P*j}r* zMg}zJ2JSpOZUjRO8#b^zwdy9)9UyZs1j=+(Lv5Z{ec-pCZc&w zL@-5i;Gv-PkDLO-sGOl(OD|?-+H6GP-KVdE^RV+bJIWDT1Cn(!>2?9HvIE(as|oQR zUk?L8d=(e+rSr@`9097A(0{?0_u3=io&;3n3FV>L&Ji3y639`z2a9_P+S2p80qUzE zngz`x^Dv!!>oMf4%C%g+FJ`bx=xUVv8SvH^TerrYeU0*82N zDJV8jYRnE8O&b7F__eY9{#d0%9ej5?reBWOd%myJSzSF)F2(_>oi{qM@Eal#_jmuu z3=|ZvZVfMaZnJPN6IM}!2V*1p%3rc;R>XBR{xCxabkK(hhq)i@52YF@8 zt`#1DvPdMuk}<1>O!|>^vmJQb88rG`o-;Y7%4Q=auxjYS!=lsz7KokWySi##yMqF7naOqv%3G*>}6Eh(q`_I+`X(!26ieK)z zS~n97FlR^?cL><-&md*wV;M3dU}d*3x;sFe7n+l>{7AsiRWY#_s-|2oDQuvpqoo;I zMX73mS9iYzG#>jYwHFoM1c^YBmX-vH@~<`R4xIvfy0n_7Xp}*+t!RP|BAn@GlK{2g z0#JYPMVN%a9ZYs2DAt83o+A3tpb+sNfv$pEVg*B4P~q}0Gp}fJ)a5%V2syP(Hr@;Z zXmwJ-CnT`n_-((63u;w0NymOqb@JFq41leYi;TCNYEc*i3AB1JnT77x@cS4bX*2JS%|f6QaEY2dRsXaY@_F&9q!V#_7p> z01meE??P`ZLRBn*uX&(K3VD-LeDjjk$@ne^lxkEg-4X=EBO0|n+aj#E;j&ZB)-01}hX_^ha%OjcI^+<3xoJ-yFN8z6ABX>4(B=mx zkFzZNMhfn(se5>)?AtP>n0|#!)(d#xNtN?>8mx1p^M`!uM3AB4z5qEGreXkjZvb!Y zC%>&iHmXaBnOaIgfN!Z7hmxyfdtZ`4W8E^d(aFBLt7(NxMW5k;^qO`GiBlxSP+I>Z zi}8Su9uM1+vCKr4^`U;qkbd(~?=kSS{`4Mc`Xq(t@(ZE&?D+H%BTW_s5!IHl^qdo^ zljGX~a-s(i8}3s&(DH+O%*ezUKH>L-ZJ_C*Wc_^{{c}B+4voU+DzI zp7c)}Zv#ede;4aj&;$G_@(zGWu$N3}sh~t6R-xds*O5gIACc`2^2?t#VHHtFd zQqCev`Ooh2pfb9`8WEj1%gA;V7rL|KGQVGvtdS-vP$W$&a&vKCC*}nO!u47Xs$=9d z<7c!w?Z~birIHFumA)647oH-YNuE`nC7v;F`ofBXgW+w6UPQJcUxbe0#whp1N|WA5 zOMDgdXW*>0TDi7dg+}jrV5b{kB;I}%0wL{^Ch)&9CI~Sz{ALL)NN|NJ7K4fKtZvb@ zQQAAGd@6_B5cAnwYRBp1?#H$D7;%u6&`)2(x1BRWYaWf$bN4=HGc3F@BmMV(j5-$R!F$ zPo|)Nx+?_zxVDqW=@X!#C5^(oA=KXFk907AqaYqaWH{iO2UnwVXsK1{5U+BTiFnhV z!l@EPOT(<+<{D8_EE2L)O;YJ>`~7HATi7<5#`=qXbTCcotQh=pe4ow!5O&GITSCgW zE9^kfzGQ1P)-U9Ja&TePJmCnRqp0>ubmm;D9*-~73;#DB$A=7Klrvd|8}_j zYvCRyi;T!&;CuCFMrJcPVmky?*pIJ?>$*m!2t!XHXYGkB;63~@Wdv9;!a+H5 zqtYhgKO|Iy4#10@#JsZBV^?&%9!rj{%5xj3LiL<{gKzMI@xJYX!3(&I;A3bQJpT`mj64D|@X$i9D(`$ATR>EVyJs?A!7JPDc-HJ8Dst|Z|Ft!xpd zs8;Pj9jSR&>)jNPsu1}KNxkKe!1(^)^Z3oU?8kD+>mm3|ISz5K*7DoH?;DEmokB^z zx;aJNOwI}E(ryF+mhg5`FS4<$q`=ie<}w!e{E6Ubx_hq>W_xhZH^8o*l6JVWhQHlc z!=psiMU--JS+t7p?QJ{Czk^y(PM1)DIGa2?Swq9qsO^m@D_k$-&Bs2SVxvNqN{U8K z1Zg%n5^}=0@yFWI{^SrE-ER7EiEnn!MAhVZD_ zZq^cPiJi(jr2Fh;<=rTbNe>Qg^mLAvBQG7l znkrF{>qf;Vdhp(A6fJmvg{i-=xHhGU00`#YOdHfNjq*Gr+wo;_nU4u5&O=7EtV|k zc2{wy)MrejC>Dd`8@b!<$FVi9d>J>po|i|Z=R^}r3+v^M+uODJEuvKov<_-tQ3&X12n!$dF@FkY-{;1T;tY|NQ)T0GR$udk*JLK zY+^F|cx@7gmk(wNsJ&~%?lp1;cGO(_8*f4m$SC}A3-@>UigUF__LMAh>m!7=h|%YT zj6!j2j<}$gGYM}XiO=0@Vef=q9%~7^kIagCGz@54(;Pe8*r?2X2|5X@6v}vJbcxS6 ziAsArij*Yg^Tfc< z9x+K`9_!b_Nxts91g9I03QmBuB?hJU$8^beuHEU5$ zZG-^Ju@?=8QB~#SS1_fc0lU27rL%G>vubsB_1=btqMAJVX|~boBcihpijZlEC=Bf& ztESodjUAGWC5Ga|j*!b2X`XHE>&hzvnXc@&~@9)!Xxd&&<`q$-Yz zGiJizb0%=Q^he6^L!l$N@T>&u1}m(&Cr-pR*p%Y z9j_)#nT$pR&rKmAP|m4QySpMH1tm&8@rG}fcD}_hUpJpoZkLcCbsyibYXb#z`$yFU z3{Wz{#o|lg4>&ph@qiul`o{K1xL@FfCEnue2gGU9Mc-uKP~n${;uG&@b~BH8U+YKA z^i-Kmb{53Ji)hzXLe5w!zgx{{Dg-A`^Iy%c?hjz@@^{xk&+~-ja5x>(D2lhN96Dt? z+(4bL+p%7(8WF3tK9;oyCxzuOcnAw$A*~!@SzB4__Oop^cIGUKTBNLmb-Mjf!!g!m zS(znwcEZjEMI@OHH0$D2{;s|=;r4??QluF@%s z3D(!>evWOkgln`}-*#$9fE2byVJ%L$F6x_3lHooOtou`<_Cm^H%V3rbcd4{1EVn}EDx^prb&*?bW+oNesNInD>VJMD zH_X*J&If%Enh^qv#jj>$-?O0(731F_pH6A1`qf>su1B!aY4V`8&GjPJrbc))Jve#4 zXZ_gesp3SGoy!>bZi1^8mO?849c77FB!G9crqPMA#ovS`yX2bA)4uCOV|Me|M0IXN znQ8p^(HQ=_T(INIAFVT}FfAn6qK}`?WzIa!5{`*d#76&R;N9Vr zZSK=^U?hg%;d!~|^j7}_X+CcKcZ}jNDYwnioeWp1NPN=-5mn)u+gir>_+e$Ln3&(% z@9VSm~pHMAa#2e#*(7xVnyo9r2G!hx^JC6&mEo8GlR1e> z)uMStw4N)FZQpd6r;Yp1e)T}C*#z$f!p}Xy+NkJU35S)OW>lLjb)6hEQP1$82`%3j z31?Aql%zS$I@5i%_NaGi*lp!bdCmE><^EpGg+4S?YN%~*nEuqmoM(7o4z-Tj5o}VS z*+K9aLboDFunpoMaq;~!?l+kp4<_vIh(GhAj~_W4U@CwcA1@pTl;0^2G#(y= zR{{Wp7qYcvH_=~ioLV9L6`>H}o?v(q64%sT(3Fv})) z*ibKi8Uml(G|`dq{G;4q$=Bk=NX62tN0;sgUs}K)!Lq9=o5w2#i-&U*Qa|R zE<8VO^A&oRQYz^G)*Rbk#dH5Jnq&N1-Om4EI_Q(j&l=k6*J*Xn1OS4;0RT`s0O$OZ zj{aUE^#9{9Ftf1!&G-0+=&Lon+?AG6_y~wOuq}}-Z=4nndPRydP|M_mXB%ZKXl)b| z8vVH!4jMV)4}udDQ+^*3fYR1^K&m4mM8YE!BNyYBK@>ogsUv`li_}iLhbW}q3T(AC zypL4*B=GjVUQKTLdLME>>7KXvT2=3?ORz}Km-wWi*)wr=Sp9frMQ)tpep$LTFUCit@ zgu(f+GkKlViB);q%A*=ZBEv#?*T_|czksCIjNP?taVyY53#ztd85~v!lZ16A}C(*>#keepZ6ie@W*xKLj-}IhWM^Z9xv|>Ysxc4oTGq91TUwt z_#|DF0!a!Al8{D%Hp5`D-l&82(f4PV(kun``OFHU@9*m>J*TF|>)} zCYf3#$EP31LFAUJmV#_Pjyd8B6y)!tV#nl(bN2&qA%6^R6TP1=X@sHs1i3&5;*R9< zBw!%4_{u<0b9Dfjy^(rQfIbNqN`sOCbfqN)znFDys2D0O32|d2r^A{ z1wA-A1FWXMcy$`Je&sPS2m)41=KmP1kfiBo6k2dOHa#V6>mca`o2^ky`N~YqErL$Kse~DkH-4rE4&$$ z!k8dEjWL1I9O~UjOO2dW^!ld`HVv_@G zT#@mxzHC=+$$6gRno2Ffa`JT}Ob7<1G9o~|%ms}bm8e@jv(e=^j1qhl1cfKByz)+H zU#vJhZ&^P2T)S)Qb${cvkT+^Q;~I>&!$k(2I85^%bTLPfn5q*N5^7VO;|~R3oW&=R z#k)yQx6u?h7eqma6b0i}J#XShk>@%&K&s&aRXv-W(bn`X?IE;9r}QG!;X&8y<2{wo1ho%R3^G5867qy#iU@XKLiislP;paJ&s`^ zZ5ozYIlkEL``2ysA$aA%GZ11^5Qv#L*!P0vDQ<8y0UcqWQn637A7q!@;a~90vYnDkM;(QwEX)#EcX2Oa=oIJByCo z)#ddj1BpSg_kkH&ra9xe0FaLR%dv-(BzI0cq!dQHkVN2vz54nv70= z%45#ENW6Y#^|C(7pk*JG$&!tL_D01%uCRl&pI3O#^>ii5K^p` zo7>^D< zIYlqL;_~8tCR|)a{vAayvN-9ZuN@A1Glrf_sukLtV~uodLFoCx9_JL$7FXJFL1t(D z5JK7|Jn>PKXmmVepCLJ7ng-g#U+4$%)f;o6i zI0tuI2#V^{!yTNNt${?&07u45fR8NNXRq49 zO`t-p)K&)LVckHtH(cETYHu~oh{DN@Y~9@}Ty5g|BzPff_v+CTr=t{A*oF6_K<7Zf>rE>Sf1>bfy#`0CCTn~4UrwN0Zcs z>OY2pyH|NOqr5&9^}!y^ifs^`J<3tv88%m5OCR_cF*bkgo!Q~NwMg@vt6Z2)J2eL2 zN*}-${rXj7hfRp;wvzRX%Pe%>^j`C^r%H{#Ekw7x2!t6_oR2l+A3s5R9P}Wsx27Fn zlJzB3N-9W=$W`!R56!-#BZw zf(BAm(9ve>@8PONfc_wlzEVB)J7LG>=Ak3zpqK_f88Q~YM!Gm7AeUEKk2L!g%@lws z9%B&3$T3ZuG_IcMRT}VKtR&olk+vkwfeCkbB8k3u668q5G%RIqw#$vtZQd^IYt&jl z*1~pP*{a#qDA0c(s;md%L? ztspoOAMRrBbpUu%nVI3(PLx*a34HUHwO|B`JF-S45jTf*f8ovg!B+BM9H}=bqGy9q z&+628U{V7_XNBD)Se^S#QJ_?>L-DCCV3-uB=dx6JC05t z#-&;8YV-LH6*{py>5?!fCN$Dw0S!NB81_JOkY(E5sIutw{J=GBf{hp>b$oY=+oirY zaJC%S#&H6JCXTr=C(KafdIV*qSA3RTsxO5nLcMlJOWh~C-HmVuNEa4G*djM<(*J~7 zNDbqAhs4q&z92d>dHWeRiN)l;3GT;&MYp2zd$csdS0y9n(^nwX9)wOTRUD)tocsIP zKsd^|xcXC?=H)SW?3{DI>2)fCEraEHS9jg*#smq&B^h})-83td*W>g0f1QtF1T0xW282O#VAaYEAqgJTgRbNj_Fz zKsalTRR%I;vbMr@1Vr+h=n&Sn6-TS)t+3>s-;}&3w^O)MB0*u2Ijn zcOF%@EC#zjpDrj;%0s_cjHd~OuZ$dKTu7Z!cH%Nr8wT~sqhggL3FH>o3Vo^^#AJ|o zy)aXiEv8#`ALSK~)iN^BnCWanCr$ifnqEvdCmyjdOesXRUlaGKYcA}}Ek0+1TQFU% zzwEbc2fuzXajkHW>;p#OCD%aNn#SCUkllvNFnjf`;&Lwtzv*7Gy8t#rWBqex7jJz$%r|VfNwPs5uiMq!4aRL?$?Br`Xonak+*lh z14v#rJ-9t9L|LFg1cjx=6?~qw2(v3tDbM%NX-b(V>tJQfZ%6V$7*ac~$!|74+Mae?@t$BZcgwxu?OnO9Su?tB!`fRU68K2`yvLAi6 z%y&w8+VM|$4$2)Rm2YINAGHXx?5v+JAC*`#=EtFEZnZlN=ioFNoZ9qrkl-YzJ{1>wQh=DSss?} zH>}p$u21B>Z?j&ij+@hwyxy>)UzqB4S|prKF`x7XkTe^Qk%mfC8dB8?Et?->tv!&Yue!5R(LprLc^R&R#adBSOHIXcKm zyLe5ukPk$S%;du9%5@aqk2ROw@lQ`DP_><4H=|jqRa25C%ERW@V2kzQDy0YSWWbsY&Y#oz z*bEke_!7g$J~4zwZA`0ljN4~#)F!pJ-rZ$u+@JkBN`1VRt-WJmY6lBvc1spAL^pwJ zZRc1G$An?b!cn!Rt_#^%vCE9cqEiOZz#1)s4c0?J5BGF8dA*>EX&oIvIhbx}8s zn##++c6^zy1;tRiSW{Ko{Yv~!6T@*h_r)?=ya+V6)L2w}=o*WzzktMbIIws^OdG0? zP`y{&S#5nJJEhDBg`7a<^7WQn>pqR&RYU8U#vq|F?;Ry( zxYh1OTCIl~mF$xoe?P#!!R)^W%5TQ7P&%y>!`wp#%GrTK0Dd9Z_@#iqK< zH$cl?nb}6(NFKTR3)G7rGWGX%=sM{7rOW2gDxoTK>JACd3aay^-=5>=yl2*)4bz86%%~MUyMg`fGN+^njHj>-J+EV4hyrySMl|+YyN5*Xr zAUPSd*gs)Me}7f^Ux86(cE*1SMqLth>@xowjBbk*Jp>wdXHp7EA{FFYSf~_OY~b{f zVJOm%#z%d;ulWj5RqGHF;!cO*?GIc`NS)RQyWz8S9$zGfUKLn6uIyB9r%$o!_*h89 zauEs`M#9Bih`6{&5M|az$q;1T%95e|;?)C@(a0s^nJfQ!O<{_|y0akXrgq``{dVSi zJ|PKrrR0W6%Le*x%6&fgeMFC=j|V)7`i;-Rob7G=#dEC9H(IRjR=qaA>&`}VBvUXV z3gzNt1a5Tp0*EBTvpxE?QtiuD(%K0})D*()I_)^tsfL3s>e5u>7W-TUQZAaa`caqz zmzvtmm#AQ{ImSqOQr2A=r zQR^5(%l47ZNj%c;H?~R`kvy4nivVZH8DBDEjJF=!Z|;NiVt|7nL3sep0Mry9W6@C< zLU{;D{`z7BszG%EL7l*M2rA+~JEf6AXUIstgpHT#%)5Di}m2hvxW=tsqW#A#hqF4SXihtIpz)<)K{uRE-Ai{#SYr+k_|*PWi$ym-EvmV1^ZRHS#hqa}+m z)orusO(gefNkg=A^ob`Zl!rcY=zSE)@9z+jY?Htl?(~zbFNiW1@8sSSa*He3il09- zQ?hWASnq0ar}RU|sJnu`wi5`Bi{V2m`|wJ3WYBaad&1_P43sDNkB%|C7-LPcreB0a zCu~?^Cw=kh^q`hPhAPg;`8K%%XRtUNomIC-H^U~qeO=U}g^T5zdXK#ZEAqr37I@aS zV>8951_I-CFmMfyej7GsxIrNjXcN7>2vVRQUgr4s#$_U7=1x7T{^SBvJ~+&H1(K6T z{_xJ%gOT{K&vi`Ik@!P5*S35Bd9pe*qlw*Gi^k12kx<>$Z=!Sw&;uIk^W-4z73@b% zsE%+52+}sSvo`gQN+I^b$w6N?FE%fV>J~L9hp9q@5g4^@q#T&8A>U34M(}>R%f*O2 zc$vO~>eep}plOoc=bWh5aALy7OpQgj4;YeTj>U$5SyN~y?~_v>vD2RWeGO4OrD|S! z=MP*RMcKTnc1)~qdGkiiU=5)`H4HGwwaP-Ce@hamoi%Dok|JvXq6X9^^xElGDA#p@ ziutm$vj>)*h>`IAKmkU`CHE%^`Rr~zL1NF92PO{%0>TEO&>e%nkuZ=`u0ni~q@+Yn zIfB?WAFK)w4-x!9jJH(6{TK?mN(IW1|LX@Xd5L=`ZY}~sm!$EBVI3vd8gz>;1wuIJ zP#L*!f&y>=eizt_aCTcBLxr0=ohv7Jn!90m^ofN0+!R(WypLi!Vr_F-n^}6CZMayL?Mam2^{dh z32|6b1JUwoo`jRd_LN^81pwIREofXaH8(a8hK`W=kuPeF5t-Czh6sH6BkPqRRS^kf=Jtwd*pyB%Nga!4{G=I zYXfr+Vki`oyo=6=kk`#iFBAG%4O=^a<557D1v9sfnmI0LZO!4^F`-zM1<&NI%F@E~ zkj0Bnz(2EfN%tq*<|)-c91!{kh=^>>xIky2$p+$C0p;9jVf8>P$F*ek5Rwm$5+VSh ziq%)Ch*2^K;DsUVBfArRinmoI;k7b8s2W~f0gF&z+=+|dlsIyhXFV&6CR$H=aJ>tG zfKUYh>XkWzQ%4EJ^#rYZ?hB;@n+GP~_AVyA=HCb@%F8>F_q)t&Z@=7TzbIsr;0(E8 zWp`DO0wf6)dw5IAh>$RGKSC?CGB`Ez8a4z36)?2-nwhxRgHAz*=o6b`)Kwi=nT+Sl z7A8_@+d)h!=eMjQRTT&l_yOk_m-I23jK#uSK!P=8Lqj>}LM(?HP>3^>Olum>SyFgc zMj@WuHV%VSh~}xuFRJjz0ea$~bS??Zo!>g$)`=HFoF#&y0Z}CU#%%p@A2x<@42ws?!ggjkh1H9TQN$-Z9tw=K! zD~JdTl@-=}A#3b)q6#-;K2e&bWv1#1bPW~BAM&V3t-X@?mOulNwzLyelz+u(m;49L z>CmhcqcR3QHNo*ylB}bfj{?x-iX(9_rtCY4-M9)!Gp^F)!$|JMMk5m35oQ55#|VTv zlf+>_Wn52Uv(Ivs=eKfsYE~HeQ}^jX3XEah>g9IQZN(H!1MuM@B{bH zAqVP{Vv$KhumJ50q41CN+K;7d$6O=Fg0D+8|AI5Tzop=&co*K2P62--TMUuMy43GD zQ}0EZ1fqPVXwYWSp3R8wN0uH6L_o)cigHea^#3W3p|b%jh+I=Zuh@%l9z||D@1zVE zo(AjQkDp?Ehr6W}34vp#c!{R23-YT5F~l8BOQ1QFfb&_%QoIG^@OlI!mO{?+hFQ#m zbB(q)3xaMj6o7|ee8DlcA0PQl!M}X`yl#*xBtJLIyk9W+(R5B(DF6rI6PX44bPy;z zaan}&9&p$n2%;&i8A5WNfRhZQ0};$6!*vo|lpINb-o$nM&(r5#ad;=8d*0k4hBGe! zN6F5@L#`z5NC_j}I2e*A2L)`~IO|PsDJ)VPv+U4i5LVr!OHh>5Fv7(~K1A?b8H_AR z@fPHx<7(g1z>(h16Aec;LCnGP00+N5r?#E7gS8L5$rCX}Q0M`fnjs>34zZ5+@${KSKGMcK0e8rklICj1_Mr;M(gz%mO1-yH+kJS|8~YFMDHk z0i0ONT6JsnLG6MaN1;F)l-O&KrS<_`>?=~@gNgi)M$Q8ou5bI}5u!6{bVi~^8;m}> zC<#IIK|~O}_b`TF7&U~5XwhX5y|;v@(OdK$UDPOJ@FwrQ|9ZdwdT+h|f33UL-FKb6 z?%DU;d)7MlyZ8ARKD;yK6p|JAfw6g|f(4T2F-Kn5G?wI%_T6D!;7J;Z<`QuRIVc4| z@nra83QidK*=bS>nBQw}GA!8q1f1ek{>6b8KSa=>OCX@CVXd1faCsmBicaNT;tJhEAqCkH#R_)9&icDs)rNi@vwR!Ig1dfGT*n(45 zK15;95iDK#Ip1LZ^$&Uq_h-N-fkGNX?V+|y#9`g{Fb6nhN4AjnbC0Kx-{K-eClZ|N z^9)+z`6ZT?{l56`DolmD*;5L#ceuCh_bkcgktSSHGW@)sfA;2b>6^C*URy!?Rh#}k zkOAR+45q6KiWMuObx!s{4Bw+MZT9+FiT?S!h*cn<;5yZ&nC`Q23ctBAwd4tI_G3^X`j+Q5fShUFg=}xC!FgwpWwf@zGmCIQY&-JT6nzJ8 z7ywgWL1XXL=C6IdS+c#faXz}S9eU1(%P^^4u-Y)S7+JU+aHvBWfK+%;92qg^j0psu zg3UV_O9Il0B9mjN)!{k!87BO0v09C1zpZ38S|&3ZfB&|Q@jz%O`?Riyg;46SkT4_9 zs1ib%kRBLIo{=z=u3Hlra%N^wN1BvjOQ@l2%;#86w5$|%8Slg?ue_>rfm!LE#;pQ3 zJ(I`05N$-BHjRY#$mPz-m5MA8UA$gR56|!E+s>3m#xr*vKY7_F_2VV1pe^V`tD|-J zCwDwBJ^Y~Tls!Efo8bW3msO$np|$DGN_3PjHD-ctKff2?Y%kUn(70auW6)VTc&eC9 zR#-4?PKx^n*r2#A4qizLC{nbhXyjH~8gV+&X6nQ@^d)3T(PlQPG3$`HA!J=@1~=b6 z>kh35hHL$5zv{h5?a#9Zy|f@ZLISGmF+&|a#zzNsiHd<-^ZZ`K66s$K$J{a-<$uv! z;7cs!Q0EbL9~KtQR*ib`y-QCPN;edP#mQejy*i~s#Fu6vDu|au2p9eDE|Z4QRmW!{ z+*lo2YFqA@E2*IX0n^Hb;Mz0R08XY5tF=K7mFmdxJ^-_VH9zCk!JIA+oz|jBVAw>< zsLrvKi`nm$_y&B;$)ZOYu=%LlOnq=`&sIG=P&L=I{DeNpiER*4BJD<2_M`|9==%Pk zbstr6Cj+)OK3lx*lysWCXLs|#$ik9N%;Bz(Y1rNSlX^D}xkPF;H_$0{{VoD*MR!gF z%onjfKHDS?kD0Ox=or(|tM-3P2z?!y+ETj^+}iop5MKR(^VMFzf_*(ra`v{sCJ?Kz zR1@8}F{gAIloDYE4ZL@Vm3Kzpp$)&SqyyNON8O+dFV*8dkxJd|C$93l_H)j;vci?i zgRM@G?3}jC`2?I!A>*lk6OQq(`Arh&2H=I&vOQ&S35`P1_hdLLA6#|8Rc*z^vn;+gXltwT?>D$l=cTo-NoLjqZcZY% z{nF5qpT*wbY$y)#tV)2HZB2f-43rfP6r~1FS)f6lBVllbA@Ii(F=M?Cz?X@7>h$dl zWv!0J{@GihLL(BJrHRQp;@;n2^ljdRLz4HH`yqb4-a*^6ko|3HXY@`qV4d;kfQ6*Y zthgipLt^pxcJa;qRbyrRQYD#@ck3zQWed=@(jca!pEaJF@td)QwVib?(24RK zoQj()N2S|PB`#?v%JsCoTsjDuCy?iDYH>K@kpd})}Jy4c? zpK#gggZ#91f?U@Nu=g{DwW0PyD9Z&&y6?A}BlGoq*JCR5zF;pM=~u*ut}d-K3%Kkx z%9?b198VLy<2WlsPgQ9J8Q$y6@BUe~ih38;nBRGDUTjbpQMPi1I@L5?(^5;!dK&jt19}8b!wq9wx2VQ z##gbuJ?5sArmZg1B)@lz=P^lL@z{y+R0(dbn__HosmVN1xpynR#ChQrx>FB$8rxl% z+S7}79eV0{IbwNB(|wNyIbmT@Yk7f2la&ZouJK$iN20cfT^#i!MmU&Hwpz}00~b?_ z!==&>4*+Y5i5cE(y`X0%FU}oqjC2Z6xw+jjsbWdxDtf1dLotn8)|zC35M-NdrhhA~ z=FCLF&2_Wci{V9M1~p;*j@m4ZC8?R*1oP-Y1){|O*2NHp65eim>%89ZzLhZtldCgr z*B_g%CF~Mpeoa2`jwZ+WFNOngbMAM(vMX!mZ~ox3ZSLJx(l;0(!U%DT#@8<667ATu z1k%V`0_``D__ho~IrBm+v+apGO4nw^H>{-=IE%aYH|s11ss%(R8$UwSjMe2we~j1m zx!LT~89R@EZyM>$m)SP1)RU>|tLhJ#%3grG3UBp*gQwksG$2)+*^9p^pEs{)fB~|- zwM^9Ku+r;}41%GSYaD3Aq>zQtP-~!K)mkd&kf0*<%>ZKplIaI49+tpH=*4dr8u z4U!^|4O16v#d9iCvbl5Ir^|lil-WSX6%KuVT&9h3;Tm`C!6i%Sb+ljg@oNDj(dP6OdUR~B#=?HAcm2GUftT$P6u_*X1wQ`tIy<+qcacw-Gs8+jRIHl^V9ex92{QaIsJ7)@-~X z$_f)XPkw5H8mR0Dj-F*nq0Hov`EshbhucHpAFSHVEdeHNMjQamUc*%%eP(~rslB3B zE{RVm>z{Pe9WNJlKrdo6))}|IRH5)@f2r?ACN7M9rx9mXy{$`t0|3}7aN56#uCyhK zrF81J>PrJR>iTuL(`Mr6?Yh&y@IH~R_3dj@XA`Ga-3Y*L%x>#Tl5ct3>fq;4x@#Qz z-B8Tw$^BmwGqz(5R%Ty0n<+U(uHT68Km)JL4CZhBn4RXw7&6PTzfn9<^V1LZU zfK~cP{F!sT&hL=+wS+2w!_GnyjUb#>3&dE8t=N6@>lu>f6Z?!@m9Jik>GqUggNd`( zgzVH>tl&^f4*O2fC`rbHtK=1Q`C;63Sle;RRS?UyQ*F3Q2SEDwMtj)Y#4hTWljluJ zms8AqtT6mrrl#oxI`v_Ey62_x=ZVVJ`stbH9%J2Hp(|GT$qh(r0&c0u7X_%wri2@Q zp-B#-=9XF(b8)mWK@~&V)S$s^YOxW9LUSSJp57KU)1rZ$Xf13kz4wzP(11SN0$2@=huMZ$`?AquT|(uzx&a<(A0 zxd#nQhYfW$t}*6NxHHD3v9tsXTPP`TF-wMD@<~DHnOjOj;aM4SbN}Hx`vXt?pCVmF zZ!bGn4<242eS0q_8|)dYIRBxxVl8DXFx3m&rfI2fV+{1Q$1+vzukW} zZ)fib#2(lf)RnMN@Bgq%dLF^6qERaE%EU50)nwM^Z%VbD<$!lRKUOH=pNM6b+(== zXsB$-Dv%Nmb~QZ?a%yfs_Z2H7`T7ClvZ#KodFiN}RIHX7QSYS_+Z z+*xhN5!NJ5`p}t~NYr`ciPW5c-B7hMH>1a3FfwQ3TsfdjF*gISed~c2(6So9njFU< zsMullOM&3Mz(Kcr9V5J7ogBJitH3vhYxlsx^Ev4+oc6o?cW$Gr)$VVKQfWpqa=+)K zw0!?C`A+u7A@^^05)U*+1(+2YBJ#(}&Js-$eIxN~4gI^FZjn3*wP7)eIl(92z>NaU zFsyU%`@EA9=)hT7<0&ft?qA5Td&E3wjJy}4O84wuVk9m~QQ@13|3L?UzXkmvHp-*_ zgNS2=TwvBZND`*2g_@oKGp+N>4#0&F7e9BXX^MABc(8dg@X7gx5*i0-R5jAPT<1Wq zHedWusw5f}GhY%p72jyS{D@roY_?a1bh$)`!cWnrf;VgRdNqDmx3Nd;n$W!XRANi% zFb|qUqukE|UcHqN9sXSRqLSG#H+_akm9oH5L0~Lpal4th;yT4iWXJ>)Ppj`MT#PXC zC(GFC+~QNkz`vd^(r$EbzIw#Jw~a20k)Kuka*Vn09k^-hIF}!~QHyKa245qZR}JeB z@J{HDirS^1W%kYbY%Mys>e4`KmwM$1Wy{)Jl;_Jg$Yti)Em{?6_S{T?%#cF>0YaUF z)q7VIlo?V%7BfW(SQ+}_=kOfzGR-{#b+fUSOT`{bdKR+h9&EL>v#osRyKa8Z=f{2q z<4nj+=&OWS&)0fL)@><0R6=wA#>5Np{*9A&TpkNQbMMJ~YE@*h7yZgHYO-FV9tczu zs$|d~j!x!*o4uo@nNej&?~al1KL9}I)p(7Y&dt=&&brs}FT|OCR?%w-t1sr+Zbi2m zBThxw66?BhED9?EG-+BKD+P&0hgA%r6^gIsVyyT`BlPM&L_VW#uv3;1Z^NLO-jbIt zzdb=x$0bMiT2q(FS}qcjyp`m;rdoa@IVVFTQ%J=i?cl@3v9QQpf_JL>Oiri91KFkE zMbkxEo}E_yTdqRM8@s(dWDS)Y0nl^iKy>=j;sZl>dH9uc=3uxkAVyW;?*>%kSOwlA zMua6l#fP4oDqBfHCdLryQ;^FtpJ(JVj7JEdc-MUYQOyQ&lEtP}5#0FTZjZ9e)D(0! z<>L3f;+;UlN}EcR*KnADt@q#u8l-+~%v^~|=GgZgE;ueTeM*6*>&b;k!>>}@tq9Dl z^bgnTkABkEA{nvrRo63!0UxX3HG8#I_Wdy%`>&PED3JUcpPDT%vQ7QmHYXxl*h_&@ zDnt}<3=RvRBWItrM3HBp$I`UjuNj}4ieb-tTOL!4jf7GCMSF7+X<^v*F$d?+%Wfu0p!h&zEJ143fEd5$~ z5WoFZShjGOnHH#u^4p|fG(JhhNc9g71)xELqyz*@Gr#yr$oCni{Nr0bFy1K((IpS5 zR4kD--oc(acg+Fi_-hJ5C-Cj<4r86JRk`P(+% zV2;+t3XO`fNrY_E5-YW+`^il7v@2MU!NS}f|1qK?)2+F1=bp>L*BAl8{oI9U*m%Ho zp)TCC$TxU@@=KjI0JFET>Oa>mpcCJDR(MZtK^!1y;(*Y!!DK#HQ(Gj$ z78Jz_sj(YtRl(l;<- zO7S7FO0mR!GJOnM<9T{pN0Ns8;PF}XtEWjtnv2@UNA><%+#QdO+2qdU=l{bh>faX% z#!qct0);eOtZn|mw3n0sVxjeV_OEP!SX0R8??8JIEY$uF%HGx03n=+d8nlMXOIM)e zKbiI#Dp)^=q6kP*NmW%zTufP2Nkv>-@!>;|vXrutvWf&qSyEI{?*HS0?dQM!M~Hx= z{#7UNmtqCl!D-#wx-?NY{)I-pov`Z$ z5;$QFWBrxvV3V^;ubggdo^a$R=*T*M3KnrcVlYYA&L3Bx&KOPB-TgGqmm&Sipl_>f zMD&wIBbo)K__Vn$lCxx~XPU#MxL%pe8|)S?3La5nV)3d#uufKlFsDr^vCU3>6~v$F zkRx}CB;a4A2{+YikbM&&f0*KFwlw-skj~=hnE%vqZfQ~oezX&T5s$lKji+Dk-52#w k+-95MWcB#>cjxJ4>EY#vUB?oOfJH^X#GITDwN;7#22H8CApigX literal 0 HcmV?d00001 diff --git a/2nd/18_Vecteur_et_coordonnées/4E_determinant_colinearite.tex b/2nd/18_Vecteur_et_coordonnées/4E_determinant_colinearite.tex new file mode 100644 index 0000000..2fb4b90 --- /dev/null +++ b/2nd/18_Vecteur_et_coordonnées/4E_determinant_colinearite.tex @@ -0,0 +1,18 @@ +\documentclass[a4paper,10pt]{article} +\usepackage{myXsim} + +\author{Benjamin Bertrand} +\title{Vecteur et coordonnées - Exercices} +\date{avril 2022} + +\DeclareExerciseCollection[step=4]{banque} +\xsimsetup{collect} + + +\begin{document} +\setcounter{exercise}{8} +\input{exercises.tex} + +\printcollection{banque} + +\end{document} diff --git a/2nd/18_Vecteur_et_coordonnées/exercises.tex b/2nd/18_Vecteur_et_coordonnées/exercises.tex index 3a5fcf7..827a196 100644 --- a/2nd/18_Vecteur_et_coordonnées/exercises.tex +++ b/2nd/18_Vecteur_et_coordonnées/exercises.tex @@ -90,7 +90,6 @@ % ------- - \begin{exercise}[subtitle={Calculs avec les coordonnées de vecteurs}, step={2}, origin={Création}, topics={ Vecteur et coordonnées }, tags={ vecteurs }] On définit les vecteurs suivants \[ @@ -153,7 +152,6 @@ % ------- - \begin{exercise}[subtitle={Norme d'un vecteur}, step={3}, origin={Création}, topics={ Vecteur et coordonnées }, tags={ vecteurs }] On définit les vecteurs suivants \[ @@ -175,3 +173,59 @@ \item Calculer la norme des vecteurs: $\vect{AB}$ et $\vect{CD}$ \end{enumerate} \end{exercise} + + +% ------- + +\begin{exercise}[subtitle={Colinéarité}, step={4}, origin={2nd math repère}, topics={ Vecteur et coordonnées }, tags={ vecteurs }] + Dans chacun des cas suivant, dire si les vecteurs $\vect{AB}$ et $\vect{AC}$ sont colinéaires + \begin{multicols}{2} + \begin{enumerate} + \item $A(1; -4)$, $B(-4; 8)$ et $C(-6; 2)$ + \item $A(5; 5)$, $B(0; -1)$ et $C(10; 11)$ + \item $A\left(\dfrac{1}{2}; \dfrac{1}{3}\right)$, $B\left(\dfrac{1}{4}; \dfrac{-2}{4}\right)$ et $C\left(\dfrac{-1}{2}; \dfrac{-11}{3}\right)$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{exercise}[subtitle={Alignement}, step={4}, origin={2nd math repère}, topics={ Vecteur et coordonnées }, tags={ vecteurs }] + Dans chacun des cas suivant, dire si les points $A$, $B$ et $C$ sont alignés + \begin{multicols}{2} + \begin{enumerate} + \item $A(4; 2)$, $B(10; -5)$ et $C(-8; 16)$ + \item $A(9; 1)$, $B(6; -1)$ et $C(3; -3)$ + \item $A\left(\dfrac{-1}{5}; 1\right)$, $B\left(2; \dfrac{-1}{6}\right)$ et $C\left(\dfrac{10}{5}; 1\right)$ + \end{enumerate} + \end{multicols} +\end{exercise} + +\begin{exercise}[subtitle={Coordonnée manquante}, step={4}, origin={2nd math repère}, topics={ Vecteur et coordonnées }, tags={ vecteurs }] + \begin{enumerate} + \item Déterminer la valeur de $m$ pour que les vecteurs $\vect{u}$ et $\vect{v}$ soient colinéaires + \begin{multicols}{2} + \begin{enumerate} + \item $\vect{u}\; \vectCoord{-8}{8}$ et $\vect{v}\; \vectCoord{m}{2}$ + \item $\vect{u}\; \vectCoord{m-1}{2}$ et $\vect{v}\; \vectCoord{3}{-2}$ + \end{enumerate} + \end{multicols} + \item Déterminer la valeur de $m$ pour que les points $A$, $B$ et $C$ soient alignés. + \begin{multicols}{2} + \begin{enumerate} + \item $A(1; 3)$, $B(-2; 1)$ et $C(m; 2)$ + \item $A(-5; 1)$, $B(7; 1)$ et $C(1; m-2)$ + \end{enumerate} + \end{multicols} + \end{enumerate} +\end{exercise} + +\begin{exercise}[subtitle={Problèmes de géométrie}, step={4}, origin={2nd math repère}, topics={ Vecteur et coordonnées }, tags={ vecteurs }] + Soit $(O, \vect{i}, \vect{h})$ un repère orthonormé. Soit $A(0; 3)$, $B(-1; 1)$ et $C(-4; 2)$ trois points. + \begin{enumerate} + \item Déterminer les coordonnées de $I$ le milieu du segment $[BC]$. + \item Déterminer les coordonnées du point $D$ tel que + \[ + 3\vect{DA}j+\vect{DB}+\vect{DC}= \vect{0} + \] + \item Démontrer que $D$, $A$ et $I$ sont alignés. + \end{enumerate} +\end{exercise} diff --git a/2nd/18_Vecteur_et_coordonnées/index.rst b/2nd/18_Vecteur_et_coordonnées/index.rst index b062647..db6a196 100644 --- a/2nd/18_Vecteur_et_coordonnées/index.rst +++ b/2nd/18_Vecteur_et_coordonnées/index.rst @@ -2,7 +2,7 @@ Vecteur et coordonnées ###################### :date: 2022-04-30 -:modified: 2022-04-30 +:modified: 2022-05-01 :authors: Benjamin Bertrand :tags: Vecteurs :category: 2nd @@ -95,5 +95,11 @@ Cours: :height: 200px :alt: cours sur le déterminant et la colinéarité +Exercices + +.. image:: ./4E_determinant_colinearite.pdf + :height: 200px + :alt: exercices sur le déterinant et la colinéarité +