Question

If $\overline{a}=2\hat{i}-3\hat{j}+5\hat{k},\overline{b}=-\hat{i}+4\hat{j}+2\hat{k}$, then the unit vector perpendicular to both $\overline{a}$ and $\overline{b}$ is

• A. $\frac{26\hat{i}+9\hat{j}-5\hat{k}}{\sqrt{782}}$
• B. $\frac{-26\hat{i}-9\hat{j}+5\hat{k}}{\sqrt{782}}$
• C. $\frac{6\hat{i}-9\hat{j}+5\hat{k}}{\sqrt{782}}$
• D. Both ($A$) and ($B$)

Answer 1

The correct option is B $\frac{-26\hat{i}-9\hat{j}+5\hat{k}}{\sqrt{782}}$

$\overrightarrow{a}\times \overrightarrow{b}=\left|\begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& -3& 5\\ -1& 4& 2\end{array}\right|=-26\hat{i}-9\hat{j}+5\hat{k}$
$|\overrightarrow{a}\times \overrightarrow{b}|=\sqrt{782}$
$\frac{\overrightarrow{a}\times \overrightarrow{b}}{|a\times \overrightarrow{b}|}=\frac{-26\hat{i}-9\hat{j}+5\hat{k}}{\sqrt{782}}$