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Update textbook.fr.md

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Claude Meny 5 years ago
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bf2c324f1c
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      00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/04.reference-frames-coordinate-systems/textbook.fr.md

7
00.brainstorming-pedagogical-teams/40.collection-existing-pedagogical-content/04.reference-frames-coordinate-systems/textbook.fr.md

@ -155,7 +155,7 @@ of the point M when only the coordinate x increases in an infinitesimal way) wri
$`\partial\overrightarrow{OM}_y=\dfrac{\partial \overrightarrow{OM}}{\partial y}\cdot dy`$, $`\partial\overrightarrow{OM}_y=\dfrac{\partial \overrightarrow{OM}}{\partial y}\cdot dy`$,
$`\quad\overrightarrow{e_y}=\dfrac{\partial\overrightarrow{OM}_y}{||\partial\overrightarrow{OM}_y||}`$<br> $`\quad\overrightarrow{e_y}=\dfrac{\partial\overrightarrow{OM}_y}{||\partial\overrightarrow{OM}_y||}`$<br>
$`\partial\overrightarrow{OM}_z=\dfrac{\partial \overrightarrow{OM}}{\partial z}\cdot dz`$, $`\partial\overrightarrow{OM}_z=\dfrac{\partial \overrightarrow{OM}}{\partial z}\cdot dz`$,
$`\overrightarrow{e_z}=\dfrac{\partial\overrightarrow{OM}_z}{||\partial\overrightarrow{OM}_z||}`$
$`\quad\overrightarrow{e_z}=\dfrac{\partial\overrightarrow{OM}_z}{||\partial\overrightarrow{OM}_z||}`$
* **N3 ($`\rightarrow`$ N4)**<br> * **N3 ($`\rightarrow`$ N4)**<br>
[ES] Los vectores $`\overrightarrow{e_x}`$, $`\overrightarrow{e_y}`$ y $`\overrightarrow{e_z}`$ [ES] Los vectores $`\overrightarrow{e_x}`$, $`\overrightarrow{e_y}`$ y $`\overrightarrow{e_z}`$
@ -170,7 +170,10 @@ En coordonnées cartésiennes, les vecteurs de base gardent la
[EN] The vectors $`\overrightarrow{e_x}`$, $`\overrightarrow{e_y}`$ y $`\overrightarrow{e_z}`$ [EN] The vectors $`\overrightarrow{e_x}`$, $`\overrightarrow{e_y}`$ y $`\overrightarrow{e_z}`$
form an **orthonormal basis** of space. It is the **base associated with Cartesian coordinates**. form an **orthonormal basis** of space. It is the **base associated with Cartesian coordinates**.
In Cartesian coordinates, the base vectors keep the In Cartesian coordinates, the base vectors keep the
**same direction whatever the position of the point $`M`$**.
**same direction whatever the position of the point $`M`$**.<br>
<br>$`(\overrightarrow{e_x},\overrightarrow{e_x},\overrightarrow{e_x})`$
base ortogonal independiente de la posición de $`M`$ / base orthogonale indépendante
de la position de $`M`$ / orthogonal basis independent of the position of $`M`$.
* **N3 ($`\rightarrow`$ N4)**<br> * **N3 ($`\rightarrow`$ N4)**<br>
[ES] La norma del vector $`\partial\overrightarrow{OM}_x=\overrightarrow{dl_x}`$ [ES] La norma del vector $`\partial\overrightarrow{OM}_x=\overrightarrow{dl_x}`$

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