Q 11-03-020NEETJEE MainEasy
The vectors $\vec{A} = a\hat{i} + 2\hat{j} - \hat{k}$ and $\vec{B} = 2a\hat{i} - a\hat{j} + 4\hat{k}$ are perpendicular to each other. The positive value of $a$ is
Answer: (A) $2$
Concept. Perpendicular vectors have zero dot product.
Step 1. Equation. $2a^2 - 2a - 4 = 0 \Rightarrow (a - 2)(a + 1) = 0$.
Step 2. Positive root. $a = 2$.
Answer. $2$ (Option A).
Solution by Sreeraj P, M.Sc Physics