Question

A unit vector perpendicular to $2\hat{i}+3\hat{j}+4\hat{k}$ and $3\hat{j}+2\hat{k}$ is given by:

• A. $\frac{(3\hat{i}+2\hat{j}-3\hat{k})}{\sqrt{22}}$
• B. $\frac{(3\hat{i}-2\hat{j}-3\hat{k})}{\sqrt{22}}$
• C. $\frac{(3\hat{i}-2\hat{j}+3\hat{k})}{\sqrt{22}}$
• D. $\frac{(-3\hat{i}+2\hat{j}+3\hat{k})}{\sqrt{22}}$

Answer 1

The correct option is A $\frac{(3\hat{i}+2\hat{j}-3\hat{k})}{\sqrt{22}}$

We have $\hat{n}=\frac{\overrightarrow{a}\times \overrightarrow{b}}{|\overrightarrow{a}\times \overrightarrow{b}|}$
$\overrightarrow{a}\times \overrightarrow{b}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& 3& 4\\ 0& 3& 2\end{array}\right|=-6\hat{i}-4\hat{j}+6\hat{k}$
$\hat{n}=\frac{6\hat{i}+4\hat{j}-6\hat{k}}{2\sqrt{22}}$
$=\frac{3\hat{i}+2\hat{j}-3\hat{k}}{\sqrt{22}}$