\( ABCDEFGH \) est un cube d'arête \( a \).
\( I \) est le milieu de \( [BC] \).
\( J \) est le milieu de \( [DH] \).
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Calculer le produit scalaire \( \overrightarrow{ JD } \cdot \overrightarrow{ JI } \) en fonction de \( a \).