If $\vec{a}=2 \hat{i}+\hat{j}+2 \hat{k}$, then the value of
$|\hat{\mathrm{i}} \times(\overrightarrow{\mathrm{a}} \times \hat{\mathrm{i}})|^{2}+|\hat{\mathrm{j}} \times(\overrightarrow{\mathrm{a}} \times \hat{\mathrm{j}})|^{2}+|\hat{\mathrm{k}} \times(\overrightarrow{\mathrm{a}} \times \hat{\mathrm{k}})|^{2} \quad$ is equal
to
$\Sigma|\vec{a}-(\vec{a} \cdot i) i|^{2}$
$\Rightarrow \quad \Sigma\left(|\mathrm{a}|^{2}+(\overrightarrow{\mathrm{a}} \cdot \mathrm{i})^{2}-2(\overrightarrow{\mathrm{a}} \cdot \mathrm{i})^{2}\right)$
$\Rightarrow \quad 3|\overrightarrow{\mathrm{a}}|^{2}-\Sigma(\overrightarrow{\mathrm{a}} \cdot \mathrm{i})^{2}$
$\Rightarrow \quad 2|\overrightarrow{\mathrm{a}}|^{2}$
$\Rightarrow \quad 18$
Click here to get exam-ready with eSaral
For making your preparation journey smoother of JEE, NEET and Class 8 to 10, grab our app now.