Q 11-03-019NEETJEE MainEasy
The angle between the vectors $\vec{A} = 2\hat{i} + 2\hat{j} - \hat{k}$ and $\vec{B} = 6\hat{i} - 3\hat{j} + 2\hat{k}$ is
Answer: (D) $\cos^{-1}\left(\dfrac{4}{21}\right)$
Concept. $\cos\theta = \dfrac{\vec A \cdot \vec B}{|\vec A||\vec B|}$.
Step 1. Values. $\vec A \cdot \vec B = 12 - 6 - 2 = 4$, $|\vec A| = 3$, $|\vec B| = 7$.
Step 2. Angle. $\cos\theta = \dfrac{4}{21}$.
Answer. $\cos^{-1}\left(\dfrac{4}{21}\right)$ (Option D).
Solution by Sreeraj P, M.Sc Physics