From 799845addf3b916cd98952da005c603f3540e3c5 Mon Sep 17 00:00:00 2001 From: Claude Meny Date: Thu, 20 Aug 2020 11:37:55 +0200 Subject: [PATCH] Update textbook.fr.md --- .../vector-analysis/textbook.fr.md | 20 +++++++++---------- 1 file changed, 9 insertions(+), 11 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 a610f06ed..a96a456df 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 @@ -510,24 +510,22 @@ tenseur de courbure, tenseur énergie-impulsion, ... ##### Componentes de un producto vectorial en base ortonormal / Composantes d'un produit vectoriel dans une base orthonormée / Components of a vector product in an orthonormal basis $`(\vec{e_1},\vec{e_2},...,\vec{e_n})`$ est une base orthonormée -$`\quad\Longrightarrow`$ $`\displaystyle\quad\forall \overrightarrow{U}\in\mathcal{P}\quad \overrightarrow{U}=\sum_{i=1}^n\;U_i\cdot\vec{e_i}`$ $`\displaystyle\quad\forall \overrightarrow{V}\in\mathcal{P}\quad \overrightarrow{V}=\sum_{i=1}^n\;V_i\cdot\vec{e_i}`$ -For the expression of a vector $`\vec{U}`$ in the base $`(\vec{e_1},\vec{e_2},...,\vec{e_n})`$, -we should use : - -$`\overrightarrow{U}=\left(\begin{array}{l}U_1//U_2//U_3)\end{array}\right)`$ - - - +* For the expression of a vector $`\vec{U}`$ in the base $`(\vec{e_1},\vec{e_2},...,\vec{e_n})`$, +we should use (?) (http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=102-03-04) :
+$`\overrightarrow{U}=\left(\begin{array}{l}U_1\\U_2\\U_3)\end{array}\right)`$ +instead of $`\overrightarrow{U}=\left|\begin{array}{l}U_1\\U_2\\U_3)\end{array}\right.`$ -méthode des produits en croix : +* méthode des produits en croix : +$`\forall\overrightarrow{U}=\left(\begin{array}{l}U_1\\U_2\\U_3)\end{array}\right)`$ et +$`\forall\overrightarrow{V}=\left(\begin{array}{l}U_1\\U_2\\U_3)\end{array}\right)`$ +$`$`\vec{U}\land\vec{V}=`$ -http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=102-03-04 -$`\overrightarrow{U}=\begin\left +$`\overrightarrow{U}=`$ method similar to the sum used to obtain the determinant of a matrix :