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) $2$
$$\vec{A}\cdot\vec{B} = 2a^2 - 2a - 4 = 0 \;\Rightarrow\; a^2 - a - 2 = 0 \;\Rightarrow\; (a - 2)(a + 1) = 0$$
The positive value is $a = 2$.
Solution by Sreeraj P, M.Sc Physics