Commit dee0cc0a authored by Claude Meny's avatar Claude Meny

Update textbook.fr.md

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...@@ -522,12 +522,12 @@ instead of $`\overrightarrow{U}=\left|\begin{array}{l}U_1\\U_2\\U_3\end{array}\r ...@@ -522,12 +522,12 @@ instead of $`\overrightarrow{U}=\left|\begin{array}{l}U_1\\U_2\\U_3\end{array}\r
[FR] méthode des produits en croix :<br> [FR] méthode des produits en croix :<br>
$`\forall\overrightarrow{U}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}`$ $`\forall\overrightarrow{U}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}`$
$`\quad\forall\overrightarrow{V}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}`$ $`\quad\forall\overrightarrow{V}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}`$
$`\quad\vec{U}\land\vec{V}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}\;\land\;\begin{pmatrix}V_1\\V_2\\V_3\end{pmatrix}`$ $`\quad\vec{U}\land\vec{V}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}\land\begin{pmatrix}V_1\\V_2\\V_3\end{pmatrix}`$
$`\quad\begin{pmatrix}U_2 V_3 - U3 V2\\U_3 V_1 - U_1 V_3\\U_1 V_2 - U_2 V_1\end{pmatrix}`$ $`\quad\begin{pmatrix}U_2 V_3 - U3 V2\\U_3 V_1 - U_1 V_3\\U_1 V_2 - U_2 V_1\end{pmatrix}`$
method similar to the sum used to obtain the determinant of a matrix : method similar to the sum used to obtain the determinant of a matrix :
$`\vec{U}\land\vec{V}=\begin{vmatrix}\overrightarrow{e_1} & overrightarrow{e_2} & overrightarrow{e_3}\\ $`\vec{U}\land\vec{V}=\begin{vmatrix} \overrightarrow{e_1}&\overrightarrow{e_2}&\overrightarrow{e_3}\\
U_1 & U_2 & U_3\\V_1 & V_2 & V_3\end{vmatrix}`$ U_1 & U_2 & U_3\\V_1 & V_2 & V_3\end{vmatrix}`$
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