For any vector $\overrightarrow{a}$, the value of $(\overrightarrow{a} \times \hat{i})^2+ (\overrightarrow{a} \times \hat{j})^2 + ( \overrightarrow{a} \times \hat{k})^2$ is equal to :

Question

( A ) $3 \overrightarrow{a}^2$
( B ) $ \overrightarrow{a}^2$
( C ) $4 \overrightarrow{a}^2$
( D ) $2 \overrightarrow{a}^2$