Question

The unit vector perpendicular to the vectors $\hat{i}-\hat{j}$ and $\hat{i}+\hat{j}$ forming a right handed system is

• A. $\hat{k}$
• B. $-2\hat{k}$
• C. $\frac{\hat{i}-\hat{j}}{\sqrt{2}}$
• D. $\frac{\hat{i}+\hat{j}}{\sqrt{2}}$

Answer 1

Answer: (A)

Required unit vector is $\pm \frac{(\hat{i}-\hat{j})\times (\hat{i}+\hat{j})}{|(\hat{i}-\hat{j})\times (\hat{i}+\hat{j})|}=\pm \frac{2\hat{k}}{2}=\pm \hat{k}$