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 7470b91e9..f2df73ece 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
@@ -515,19 +515,15 @@ $`\displaystyle\quad\forall \overrightarrow{V}\in\mathcal{P}\quad \overrightarro
 
 * [FR] For the expression of a vector $`\vec{U}`$ in the base $`(\vec{e_1},\vec{e_2},...,\vec{e_n})`$,
 we shouldn't we use (http://www.electropedia.org/iev/iev.nsf/display?openform&ievref=102-03-04) : <br>
-$`\overrightarrow{U}=\left(\begin{array}{l}U_1\\U_2\\U_3\end{array}\right)`$
-$`\displaystyle\overrightarrow{U}=\left(\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}\right)`$
+$`\overrightarrow{U}=\begin{pmatrix}U_1\\U_2\\U_3\end{pmatrix}`$ or $`\overrightarrow{U}=\begin{bmatrix}U_1\\U_2\\U_3\end{bmatrix}`$
 instead of $`\overrightarrow{U}=\left|\begin{array}{l}U_1\\U_2\\U_3\end{array}\right.`$ as we do at INSA ?
 
 * [ES]  <br>
 [FR] méthode des produits en croix :<br>
-$`\forall\overrightarrow{U}=\left(\begin{array}{l}U_1\\U_2\\U_3\end{array}\right)`$ et
-$`\forall\overrightarrow{V}=\left(\begin{array}{l}U_1\\U_2\\U_3\end{array}\right)`$
-$`$`\vec{U}\land\vec{V}=`$
-
-
-$`\overrightarrow{U}=`$
-
+$`\forall\overrightarrow{U}=\begin{pmatrix}{l}U_1\\U_2\\U_3\end{pmatrix}`$ 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}`$
+$`\quad\begin{pmatrix}{l}U_2 V_3 - U3 V2\\U_3 V_1 - U_1 V_3\\U_1 V_2 - U_2 V_1\end{pmatrix}`$
 
 method similar to the sum used to obtain the determinant of a matrix :