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 f2df73ece..7d45de56d 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
@@ -520,15 +520,14 @@ instead of $`\overrightarrow{U}=\left|\begin{array}{l}U_1\\U_2\\U_3\end{array}\r
 
 * [ES]  <br>
 [FR] méthode des produits en croix :<br>
-$`\forall\overrightarrow{U}=\begin{pmatrix}{l}U_1\\U_2\\U_3\end{pmatrix}`$ et
-$`\forall\overrightarrow{V}=\begin{pmatrix}{l}U_1\\U_2\\U_3\end{pmatrix}`$
-$`$`\vec{U}\land\vec{V}=\begin{pmatrix}{l}U_1\\U_2\\U_3\end{pmatrix}\land\begin{pmatrix}{l}V_1\\V_2\\V_3\end{pmatrix}`$
-$`\quad\begin{pmatrix}{l}U_2 V_3 - U3 V2\\U_3 V_1 - U_1 V_3\\U_1 V_2 - U_2 V_1\end{pmatrix}`$
+$`\forall\overrightarrow{U}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}`$
+$`\quad\forall\overrightarrow{V}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}`$
+$`\quad\vec{U}\land\vec{V}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}\;\land\;\begin{pmatrix}V_1\\V_2\\V_3\end{pmatrix}`$
+$`\quad\begin{pmatrix}U_2 V_3 - U3 V2\\U_3 V_1 - U_1 V_3\\U_1 V_2 - U_2 V_1\end{pmatrix}`$
 
 method similar to the sum used to obtain the determinant of a matrix :
 
-
-**$`\displaystyle\quad\overrightarrow{U}\cdot\overrightarrow{V}=U_1\,V_1 + U_2\,V_2 + ... + U_n\,V_n = \sum_{i=1}^n\;U_i\,V_i`$**
+$`\vec{U}\land\vec{V}=\begin{vmatrix}\vec{e_1} vec{e_2} vec{e_3}\\U_1 U_2 U_3\\V_1 V_2 V_3\end{pmatrix}`$