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Update textbook.fr.md

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Claude Meny 5 years ago
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      00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/05.classical-mechanics/vector-analysis/textbook.fr.md

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00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/05.classical-mechanics/vector-analysis/textbook.fr.md

@ -518,16 +518,17 @@ we shouldn't we use (http://www.electropedia.org/iev/iev.nsf/display?openform&ie
$`\overrightarrow{U}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}`$ or $`\overrightarrow{U}=\begin{bmatrix}U_1\\U_2\\U_3\end{bmatrix}`$
instead of $`\overrightarrow{U}=\left|\begin{array}{l}U_1\\U_2\\U_3\end{array}\right.`$ as we do at INSA ?
* [ES] <br>
c
[FR] méthode des produits en croix :<br>
$`\forall\overrightarrow{U}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}`$
$`\quad\forall\overrightarrow{V}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}`$
$`\quad\vec{U}\land\vec{V}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}\land\begin{pmatrix}V_1\\V_2\\V_3\end{pmatrix}`$
$`\quad\begin{pmatrix}U_2 V_3 - U3 V2\\U_3 V_1 - U_1 V_3\\U_1 V_2 - U_2 V_1\end{pmatrix}`$
method similar to the sum used to obtain the determinant of a matrix :
$`\quad\begin{pmatrix}U_2 V_3 - U_3 V_2\\U_3 V_1 - U_1 V_3\\U_1 V_2 - U_2 V_1\end{pmatrix}`$
$`\vec{U}\land\vec{V}=\begin{vmatrix} \overrightarrow{e_1}&\overrightarrow{e_2}&\overrightarrow{e_3}\\
* [ES] <br>
[FR] <br>
[EN] method similar to the sum used to obtain the determinant of a matrix :<br>
<br>$`\vec{U}\land\vec{V}=\begin{vmatrix} \overrightarrow{e_1}&\overrightarrow{e_2}&\overrightarrow{e_3}\\
U_1 & U_2 & U_3\\V_1 & V_2 & V_3\end{vmatrix}`$

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