63 lines
1.8 KiB
TeX
63 lines
1.8 KiB
TeX
\documentclass[a4paper,10pt]{article}
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\usepackage{myXsim}
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\title{Exercices produit scalaire coordonnée}
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\tribe{1ST}
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\date{Novembre 2019}
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\pagestyle{empty}
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%\geometry{left=15mm,right=15mm, bottom=8mm, top=5mm}
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\begin{document}
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\begin{exercise}[subtitle={Projeté orthogonal}]
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\begin{minipage}{0.5\textwidth}
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On considère la figure ci-contre, l'unité de longueur étant le côté d'un carreau.
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Calculer les produits scalaires suivants
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\begin{enumerate}
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\item $\vec{AB}.\vec{AC}$
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\item $\vec{AD}.\vec{DC}$
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\end{enumerate}
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\end{minipage}
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\hfill
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\begin{minipage}{0.4\textwidth}
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\begin{tikzpicture}[scale=0.6]
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\tkzInit[xmin=0,xmax=6,xstep=1,
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ymin=0,ymax=4,ystep=1]
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\tkzGrid
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\draw (1, 1) node {x} node[below left] {$A$};
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\draw (5, 1) node {x} node[below left] {$B$};
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\draw (2, 3) node {x} node[below left] {$C$};
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\draw (3, 1) node {x} node[below left] {$D$};
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\draw (2, 1) node {x} node[below left] {$E$};
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\end{tikzpicture}
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\end{minipage}
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\end{exercise}
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\begin{exercise}[subtitle={Formule du Cos}]
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\begin{enumerate}
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\item Soit $||\vec{u}|| = \sqrt{2}$, $||\vec{v}||=6$ et $(\vec{u};\vec{v}) = -\dfrac{\pi}{6}$. Calculer $\vec{u}.\vec{v}$.
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\item Soit $||\vec{u}|| = 2$, $\vec{u}.\vec{v} = -10$ et $(\vec{u};\vec{v}) = \pi$. Calculer $||\vec{v}||$.
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\item Soit $||\vec{u}|| = \sqrt{2}$, $||\vec{v}||=1$ et $\vec{u}.\vec{v} = 1$. Calculer $\cos(\vec{u};\vec{v})$ puis en déduire $(\vec{u};\vec{v})$.
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\end{enumerate}
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\end{exercise}
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\vfill
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\printexercise{exercise}{1}
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\printexercise{exercise}{2}
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\vfill
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\printexercise{exercise}{1}
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\printexercise{exercise}{2}
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\vfill
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\printexercise{exercise}{1}
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\printexercise{exercise}{2}
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\end{document}
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