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

Answer 1

The correct option is A

$\hat{k}$

Explanation for correct option

Let the vector perpendicular to the vectors $\hat{i}-\hat{j}$ and $\hat{i}+\hat{j}$ is $\overrightarrow{r}$.

Vector $\overrightarrow{r}=(\hat{i}-\hat{j})\times (i+\hat{j})=2\hat{k}$

$\left|\overrightarrow{r}\right|=2$

Therefore, unit vector $\hat{r}=\frac{\overrightarrow{r}}{\left|\overrightarrow{r}\right|}$

$$\begin{gathered} =\frac{2\hat{k}}{2} \\ =\hat{k} \end{gathered}$$

Hence, the correct option is $\mathrm{Option}\left(\mathrm{A}\right)$