Question

The unit vector perpendicular to both of the vectors 2 $\hat{i}-\hat{j}+\hat{k}$ and $3\hat{i}+4\hat{j}-\hat{k}$ is

• A. $\pm \frac{(-3\hat{i}+5\hat{j}+11\hat{k})}{\sqrt{155}}$
• B. $\pm (-3\hat{i}+5\hat{i}+11\hat{k})$
• C. $\pm \frac{(-3\hat{i}-5\hat{j}+11\hat{k})}{\sqrt{155}}$
• D. $\pm \frac{(-3\hat{i}+5\hat{j}+11\hat{k})}{\sqrt{156}}$

Answer 1

Answer: (A)

$\pm \frac{(-3\hat{i}+5\hat{j}+11\hat{k})}{\sqrt{155}}$

$\overrightarrow{V}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& -1& 1\\ 3& 4& 1\end{array}\right|=-3\hat{i}+5\hat{j}+11\hat{k}$
$|\overrightarrow{V}|=\sqrt{155}$
Unit Vector is given by
$\frac{\overrightarrow{V}}{|\overrightarrow{V}|}{=}_{-}^{+}\frac{(-3\hat{i}+5\hat{j}+11\hat{k})}{\sqrt{155}}$