From c050e2dce0ddf1d41bd80f2c9422681d2e632298 Mon Sep 17 00:00:00 2001 From: Claude Meny Date: Sun, 30 Aug 2020 19:14:10 +0200 Subject: [PATCH] Update textbook.fr.md --- .../04.reference-frames-coordinate-systems/textbook.fr.md | 5 +++-- 1 file changed, 3 insertions(+), 2 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 fafe23f3b..3abd02884 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 @@ $`=dx\;\overrightarrow{e_x}+dy\;\overrightarrow{e_y}+dz\;\overrightarrow{e_z}`$<
$`||\overrightarrow{dl}||=\sqrt{\overrightarrow{dl}\cdot\overrightarrow{dl}}`$ $`=\sqrt{(dl_x\;\overrightarrow{e_x}+dl_y\;\overrightarrow{e_y}+dl_z\;\overrightarrow{e_z})\cdot (dl_x\;\overrightarrow{e_x}+dl_y\;\overrightarrow{e_y}+dl_z\;\overrightarrow{e_z})}`$ -$`=\sqrt{(dl_x)^2\;(\overrightarrow{e_x}\cdot\overrightarrow{e_x})+(dl_y)^2\;(\overrightarrow{e_y}\cdot\overrightarrow{e_y}) +$`=\left[(dl_x)^2\;(\overrightarrow{e_x}\cdot\overrightarrow{e_x})\right.$` +`$+(dl_y)^2\;(\overrightarrow{e_y}\cdot\overrightarrow{e_y}) +(dl_z)^2\;(\overrightarrow{e_z}\cdot\overrightarrow{e_z})}`$ $`+(2\,dl_x\,dl_y)\,(\overrightarrow{e_x}\cdot\overrightarrow{e_y})`$ $`+(2\,dl_x\,dl_z)\,(\overrightarrow{e_x}\cdot\overrightarrow{e_z})`$ -$`+(2\,dl_y\,dl_z)\,(\overrightarrow{e_y}\cdot\overrightarrow{e_z})`$ +$`\left.+(2\,dl_y\,dl_z)\,(\overrightarrow{e_y}\cdot\overrightarrow{e_z})\right]^{1/2}`$ $`=\sqrt{(dl_x)^2+(dl_y)^2+(dl_z)^2}`$ $`=\sqrt{dx^2+dy^2+dz^2}=dl`$