Question

What is the unit vector perpendicular to the following vectors 2$\hat{i}$ + 2$\hat{j}$ - $\hat{k}$ and 6$\hat{i}$ - 3$\hat{j}$ + 2$\hat{k}$

• A.
• B.
• C.
• D.

Answer 1

The correct option is C

$\overline{A}$ = 2$\hat{i}$ + 2$\hat{j}$ - $\hat{k}$ and $\overline{B}$ = 6$\hat{i}$ - 3$\hat{j}$ + 2$\hat{k}$
$\overline{C}$ = $\overline{A}$ $\times$ $\overline{B}$ = ( 2$\hat{i}$ + 2$\hat{j}$ - $\hat{k}$) $\times$ (6$\hat{i}$ - 3$\hat{j}$ +2$\hat{k}$)
= $\lceil \begin{array}{ccc}\hat{i}& \hat{j}& \hat{k}\\ 2& 2& -1\\ 6& -3& 2\end{array}\rceil$ = $\hat{i}$ - 10$\hat{j}$ - 18$\hat{k}$
Unit vector perpendicular to both $\overline{A}$ and $\overline{B}$
= $\frac{\hat{i}-10\hat{j}-18\hat{k}}{\sqrt{1^2+{10}^2+{18}^2}}$ = $\frac{\hat{i}-10\hat{j}-18\hat{k}}{5\sqrt{17}}$