From 0d3c8759dbfd9e1f8e9e0e37704789afecc4390a Mon Sep 17 00:00:00 2001
From: Claude Meny <claude.meny@irap.omp.eu>
Date: Tue, 18 Aug 2020 17:43:03 +0200
Subject: [PATCH] Update textbook.fr.md

---
 .../vector-analysis/textbook.fr.md                 | 14 +++++++++-----
 1 file changed, 9 insertions(+), 5 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 57d3ff7a1..bfb7eda6a 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
@@ -419,15 +419,19 @@ $`\displaystyle\quad\overrightarrow{U}\cdot\overrightarrow{V}=U_1\,V_1 + U_2\,V_
 $`\left.\begin{array}{l}\overrightarrow{U}\cdot\overrightarrow{V}=||\overrightarrow{U}||\cdot||\overrightarrow{V}||\cdot 
 cos (\widehat{\overrightarrow{U},\overrightarrow{V}}) \\
 \overrightarrow{U}\cdot\overrightarrow{V}=U_1\,V_1 + U_2\,V_2 + U_3\,V_3\end{array}\right|`$
-
-
-
 $`\quad\Longrightarrow`$
-$`\quad cos (\widehat{\overrightarrow{U},\overrightarrow{V}})=\dfrac{U_1\,V_1 + U_2\,V_2 + U_3\,V_3}{||\overrightarrow{U}||\cdot||\overrightarrow{V}||}`$
+$`\quad cos (\widehat{\overrightarrow{U},\overrightarrow{V}})=\dfrac{\overrightarrow{U}\cdot\overrightarrow{V}}
+{||\overrightarrow{U}||\cdot||\overrightarrow{V}||}`$
+$`\quad\Longrightarrow`$
+$`\quad cos (\widehat{\overrightarrow{U},\overrightarrow{V}})=\dfrac{U_1\,V_1 + U_2\,V_2 + U_3\,V_3}
+{||\overrightarrow{U}||\cdot||\overrightarrow{V}||}`$
+$`\quad\Longrightarrow`$
+$`\quad \widehat{\overrightarrow{U},\overrightarrow{V}}= arcos\left(\dfrac{\overrightarrow{U}\cdot\overrightarrow{V}}
+{||\overrightarrow{U}||\cdot||\overrightarrow{V}||}\right)`$
+$`\quad\Longrightarrow`$
 $`\quad \widehat{\overrightarrow{U},\overrightarrow{V}}= arcos\left(\dfrac{U_1\,V_1 + U_2\,V_2 + U_3\,V_3}
 {||\overrightarrow{U}||\cdot||\overrightarrow{V}||}\right)`$
 
-
 #### Produit vectoriel de 2 vecteurs
 
 ##### Produit vectoriel de 2 vecteurs dans une base quelconque