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_
 $`\left.\begin{array}{l}\overrightarrow{U}\cdot\overrightarrow{V}=||\overrightarrow{U}||\cdot||\overrightarrow{V}||\cdot 
 cos (\widehat{\overrightarrow{U},\overrightarrow{V}}) \\
 \overrightarrow{U}\cdot\overrightarrow{V}=U_1\,V_1 + U_2\,V_2 + U_3\,V_3\end{array}\right|`$
-
-
-
 $`\quad\Longrightarrow`$
-$`\quad cos (\widehat{\overrightarrow{U},\overrightarrow{V}})=\dfrac{U_1\,V_1 + U_2\,V_2 + U_3\,V_3}{||\overrightarrow{U}||\cdot||\overrightarrow{V}||}`$
+$`\quad cos (\widehat{\overrightarrow{U},\overrightarrow{V}})=\dfrac{\overrightarrow{U}\cdot\overrightarrow{V}}
+{||\overrightarrow{U}||\cdot||\overrightarrow{V}||}`$
+$`\quad\Longrightarrow`$
+$`\quad cos (\widehat{\overrightarrow{U},\overrightarrow{V}})=\dfrac{U_1\,V_1 + U_2\,V_2 + U_3\,V_3}
+{||\overrightarrow{U}||\cdot||\overrightarrow{V}||}`$
+$`\quad\Longrightarrow`$
+$`\quad \widehat{\overrightarrow{U},\overrightarrow{V}}= arcos\left(\dfrac{\overrightarrow{U}\cdot\overrightarrow{V}}
+{||\overrightarrow{U}||\cdot||\overrightarrow{V}||}\right)`$
+$`\quad\Longrightarrow`$
 $`\quad \widehat{\overrightarrow{U},\overrightarrow{V}}= arcos\left(\dfrac{U_1\,V_1 + U_2\,V_2 + U_3\,V_3}
 {||\overrightarrow{U}||\cdot||\overrightarrow{V}||}\right)`$
 
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 #### Produit vectoriel de 2 vecteurs
 
 ##### Produit vectoriel de 2 vecteurs dans une base quelconque