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keep-around/e2d796c943a5d9286bc38f03db8736c8d230a73a
Claude Meny 5 years ago
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e2d796c943
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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

@ -523,13 +523,14 @@ c
$`\forall\overrightarrow{U}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}`$ $`\forall\overrightarrow{U}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}`$
$`\quad\forall\overrightarrow{V}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}`$ $`\quad\forall\overrightarrow{V}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}`$
$`\quad\vec{U}\land\vec{V}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}\land\begin{pmatrix}V_1\\V_2\\V_3\end{pmatrix}`$ $`\quad\vec{U}\land\vec{V}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}\land\begin{pmatrix}V_1\\V_2\\V_3\end{pmatrix}`$
$`\quad\begin{pmatrix}U_2 V_3 - U_3 V_2\\U_3 V_1 - U_1 V_3\\U_1 V_2 - U_2 V_1\end{pmatrix}`$
$`\quad=±,\begin{pmatrix}U_2 V_3 - U_3 V_2\\U_3 V_1 - U_1 V_3\\U_1 V_2 - U_2 V_1\end{pmatrix}`$
* [ES] <br> * [ES] <br>
[FR] <br> [FR] <br>
[EN] method similar to the sum used to obtain the determinant of a matrix :<br> [EN] method similar to the sum used to obtain the determinant of a matrix :<br>
<br>$`\vec{U}\land\vec{V}=\begin{vmatrix} \overrightarrow{e_1}&\overrightarrow{e_2}&\overrightarrow{e_3}\\ <br>$`\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}`$ U_1 & U_2 & U_3\\V_1 & V_2 & V_3\end{vmatrix}`$
$`=U_1V_1\overrightarrow{e_3}+U_2V_3\overrightarrow{e_1}+U_2V_3\overrightarrow{e_1}`$

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