Question

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

• A. $\overline{k}$
• B. $-\overline{k}$
• C. $\frac{1}{\sqrt{2}}(\overline{i}-\overline{j})$
• D. $\frac{1}{\sqrt{2}}(\overline{i}+\overline{j})$

Answer 1

The correct option is A $\overline{k}$

Vector perpendicular to $a=\overrightarrow{i}-\overrightarrow{j}$ and $b=\overrightarrow{i}+\overrightarrow{j}$ is $c=a\times b$

$c=a\times b=2\overrightarrow{k}$ and unit vector in the direction

of $c$ is $\overrightarrow{k}$

option A gives correct answer