Question

The unit vector perpendicular to $\hat{i}-\hat{j}$ and coplanar with $\hat{i}+2\hat{j}$ and $2\hat{i}+3\hat{j}$ is :

• A. $\frac{2\hat{i}-5\hat{j}}{\sqrt{29}}$
• B. $2\hat{i}+5\hat{j}$
• C. $\frac{1}{\sqrt{2}}\left(\hat{i}+\hat{j}\right)$
• D. $\hat{i}+\hat{j}$

Answer 1

Answer: (C)

Let the unit vector $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$ is perpendicular to $\hat{i}-\hat{j}$, then we get
$\frac{\left(\hat{i}+\hat{j}\right)\cdot \left(\hat{i}-\hat{j}\right)}{\sqrt{2}}=\frac{1-1}{\sqrt{2}}=0$
$\therefore \frac{\hat{i}+\hat{j}}{\sqrt{2}}$ is the unit vector