jee-main 2025 Q12

jee-main · India · session1_24jan_shift2 Vectors 3D & Lines Vector Algebra and Triple Product Computation
Let $\vec{\mathrm{a}} = 3\hat{i} - \hat{j} + 2\hat{k}$, $\vec{\mathrm{b}} = \vec{\mathrm{a}} \times (\hat{i} - 2\hat{k})$ and $\vec{\mathrm{c}} = \vec{\mathrm{b}} \times \hat{k}$. Then the projection of $\vec{\mathrm{c}} - 2\hat{j}$ on $\vec{a}$ is:
(1) $2\sqrt{14}$
(2) $\sqrt{14}$
(3) $3\sqrt{7}$
(4) $2\sqrt{7}$
Let $\vec{\mathrm{a}} = 3\hat{i} - \hat{j} + 2\hat{k}$, $\vec{\mathrm{b}} = \vec{\mathrm{a}} \times (\hat{i} - 2\hat{k})$ and $\vec{\mathrm{c}} = \vec{\mathrm{b}} \times \hat{k}$. Then the projection of $\vec{\mathrm{c}} - 2\hat{j}$ on $\vec{a}$ is:\\
(1) $2\sqrt{14}$\\
(2) $\sqrt{14}$\\
(3) $3\sqrt{7}$\\
(4) $2\sqrt{7}$