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