From 96a6f168ad0512223f28b9064789f901c262b01c Mon Sep 17 00:00:00 2001 From: Claude Meny Date: Thu, 20 Aug 2020 18:58:21 +0200 Subject: [PATCH] Update textbook.fr.md --- .../vector-analysis/textbook.fr.md | 11 +++++------ 1 file changed, 5 insertions(+), 6 deletions(-) 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 f2df73ece..7d45de56d 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 @@ -520,15 +520,14 @@ instead of $`\overrightarrow{U}=\left|\begin{array}{l}U_1\\U_2\\U_3\end{array}\r * [ES]
[FR] méthode des produits en croix :
-$`\forall\overrightarrow{U}=\begin{pmatrix}{l}U_1\\U_2\\U_3\end{pmatrix}`$ et -$`\forall\overrightarrow{V}=\begin{pmatrix}{l}U_1\\U_2\\U_3\end{pmatrix}`$ -$`$`\vec{U}\land\vec{V}=\begin{pmatrix}{l}U_1\\U_2\\U_3\end{pmatrix}\land\begin{pmatrix}{l}V_1\\V_2\\V_3\end{pmatrix}`$ -$`\quad\begin{pmatrix}{l}U_2 V_3 - U3 V2\\U_3 V_1 - U_1 V_3\\U_1 V_2 - U_2 V_1\end{pmatrix}`$ +$`\forall\overrightarrow{U}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}`$ +$`\quad\forall\overrightarrow{V}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}`$ +$`\quad\vec{U}\land\vec{V}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}\;\land\;\begin{pmatrix}V_1\\V_2\\V_3\end{pmatrix}`$ +$`\quad\begin{pmatrix}U_2 V_3 - U3 V2\\U_3 V_1 - U_1 V_3\\U_1 V_2 - U_2 V_1\end{pmatrix}`$ method similar to the sum used to obtain the determinant of a matrix : - -**$`\displaystyle\quad\overrightarrow{U}\cdot\overrightarrow{V}=U_1\,V_1 + U_2\,V_2 + ... + U_n\,V_n = \sum_{i=1}^n\;U_i\,V_i`$** +$`\vec{U}\land\vec{V}=\begin{vmatrix}\vec{e_1} vec{e_2} vec{e_3}\\U_1 U_2 U_3\\V_1 V_2 V_3\end{pmatrix}`$