Question Statement:
Let $\hat{i}, \hat{j}$, and $\hat{k}$ be the unit vectors in the $x, y$ and $z$ directions, respectively. If the vector $\hat{i} + \hat{j}$ is rotated about positive $\hat{k}$ by $135^\circ$, one gets:
Scientific schematic diagram reproduced from official IIT paper
Options:
- (A) $-\hat{i}$
- (B) $-\hat{j}$
- (C) $-\frac{1}{\sqrt{2}}\hat{j}$
- (D) $-\sqrt{2}\hat{i}$