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 091c550bc..19e2f623a 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
@@ -509,7 +509,13 @@ 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
 
-Base orthonormée $`(\vec{e_1},\vec{e_2},\vec{e_3})`$
+"$`(\vec{e_1},\vec{e_2},...,\vec{e_n})`$ est une base orthonormée.
+$`\quad\Longrightarrow`$
+$`\displaystyle\quad\forall \overrightarrow{U}\in\mathcal{P}\quad \overrightarrow{U}=\sum_{i=1}^n\;U_i\cdot\vec{e_i}`$ 
+$`\displaystyle\quad\forall \overrightarrow{V}\in\mathcal{P}\quad \overrightarrow{V}=\sum_{i=1}^n\;V_i\cdot\vec{e_i}`$  
+**$`\displaystyle\quad\overrightarrow{U}\cdot\overrightarrow{V}=U_1\,V_1 + U_2\,V_2 + ... + U_n\,V_n = \sum_{i=1}^n\;U_i\,V_i`$**
+
+