Question

The vector $\overrightarrow{O A}$ where $O$ is origin is given by $\overrightarrow{O A}=2 \hat{i}+2 \hat{j}$. Now it is rotated by $45^{\circ}$ anticlockwise about $O$. What will be the new vector?

• A. $2 \sqrt{2} \hat{j}$
• B. $2 \hat{j}$
• C. $2 \hat{i}$
• D. $2 \sqrt{2} \hat{i}$

Answer 1

Answer: (A)

$\overrightarrow{ OA }=2 \hat{i}+2 \hat{j}$
$|\overrightarrow{O A}|=\sqrt{4+4}$
$\Rightarrow 2 \sqrt{2}$
On rotating by an angle of $45^{\circ}$ anticlockwise it will lie along $y$-axis.
So $\vec{A}=2 \sqrt{2} \hat{j}$