From 159ba6696f7952fe1380d2f1148471277977da23 Mon Sep 17 00:00:00 2001 From: Claude Meny Date: Sun, 30 Aug 2020 19:00:03 +0200 Subject: [PATCH] Update textbook.fr.md --- .../textbook.fr.md | 11 ++++++----- 1 file changed, 6 insertions(+), 5 deletions(-) diff --git a/00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/04.reference-frames-coordinate-systems/textbook.fr.md b/00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/04.reference-frames-coordinate-systems/textbook.fr.md index 4aea3a6f4..c2e4be83e 100644 --- a/00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/04.reference-frames-coordinate-systems/textbook.fr.md +++ b/00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/04.reference-frames-coordinate-systems/textbook.fr.md @@ -256,11 +256,12 @@ $`=dx\;\overrightarrow{e_x}+dy\;\overrightarrow{e_y}+dz\;\overrightarrow{e_z}`$<
$`||\overrightarrow{dl}||=\sqrt{\overrightarrow{dl}\cdot\overrightarrow{dl}}`$ $`=\sqrt{(dl_x\;\overrightarrow{e_x}+dl_y\;\overrightarrow{e_y}+dl_z\;\overrightarrow{e_z})\cdot (dl_x\;\overrightarrow{e_x}+dl_y\;\overrightarrow{e_y}+dl_z\;\overrightarrow{e_z})}`$ -$`=\sqrt{dl_x^2\;(\overrightarrow{e_x}\cdot\overrightarrow{e_x})+dl_y^2\;(\overrightarrow{e_y}\cdot\overrightarrow{e_y}) +dl_z^2\;(\overrightarrow{e_z}\cdot\overrightarrow{e_z})`$ -$`+2\,dl_x\,dl_y\,x(\overrightarrow{e_x}\cdot\overrightarrow{e_y})`$ -$`+2\,dl_x\,dl_z\,x(\overrightarrow{e_x}\cdot\overrightarrow{e_z})`$ -$`+2\,dl_y\,dl_z\,x(\overrightarrow{e_y}\cdot\overrightarrow{e_z})}`$ -$`=\sqrt{dl_x^2+dl_y^2+dl_z^2}`$ +$`=\sqrt{(dl_x)^2\;(\overrightarrow{e_x}\cdot\overrightarrow{e_x})+(dl_y)^2\;(\overrightarrow{e_y}\cdot\overrightarrow{e_y}) ++(dl_z)^2\;(\overrightarrow{e_z}\cdot\overrightarrow{e_z})`$ +$`+(2\,dl_x\,dl_y)\,(\overrightarrow{e_x}\cdot\overrightarrow{e_y})`$ +$`+(2\,dl_x\,dl_z)\,(\overrightarrow{e_x}\cdot\overrightarrow{e_z})`$ +$`+(2\,dl_y\,dl_z)\,(\overrightarrow{e_y}\cdot\overrightarrow{e_z})}`$ +$`=\sqrt{(dl_x)^2+(dl_y)^2+(dl_z)^2}`$ $`=\sqrt{dx^2+dy^2+dz^2}`$