diff --git a/00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/05.classical-mechanics/vector-analysis/textbook.fr.md b/00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/05.classical-mechanics/vector-analysis/textbook.fr.md index 1dc70573e..c16e5d368 100644 --- a/00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/05.classical-mechanics/vector-analysis/textbook.fr.md +++ b/00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/05.classical-mechanics/vector-analysis/textbook.fr.md @@ -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 :
$`\forall\overrightarrow{U}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}`$ $`\quad\forall\overrightarrow{V}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}`$ -$`\quad\vec{U}\land\vec{V}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}\;\land\;\begin{pmatrix}V_1\\V_2\\V_3\end{pmatrix}`$ +$`\quad\vec{U}\land\vec{V}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}\land\begin{pmatrix}V_1\\V_2\\V_3\end{pmatrix}`$ $`\quad\begin{pmatrix}U_2 V_3 - U3 V2\\U_3 V_1 - U_1 V_3\\U_1 V_2 - U_2 V_1\end{pmatrix}`$ method similar to the sum used to obtain the determinant of a matrix : -$`\vec{U}\land\vec{V}=\begin{vmatrix}\overrightarrow{e_1} & overrightarrow{e_2} & overrightarrow{e_3}\\ +$`\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}`$