Question

Let $\overrightarrow{a}\left(3\hat{i}22\hat{j}22\hat{k}\hat{b}\right(\hat{i}22\hat{j}2\hat{k}.$ Then a unit vector perpendicular to both $\overrightarrow{a}\overrightarrow{b}$ and $\overrightarrow{a}2\overrightarrow{b}$ is

• A. $\frac{1}{3}\left(2\hat{i}22\hat{j}2\hat{k}\right)$
• B. $\frac{1}{3}\left(2\hat{i}22\hat{j}\hat{k}\right)$
• C. $\frac{1}{3}\left(2\hat{i}2\hat{j}2\hat{k}\right)$
• D. $\frac{1}{3}\left(\hat{i}2\hat{j}2\hat{k}\right)$

Answer 1

The correct option is A $\frac{1}{3}\left(2\hat{i}22\hat{j}2\hat{k}\right)$

$\left(\overrightarrow{a}\overrightarrow{b}\right)\times \left(\overrightarrow{a}4\overrightarrow{b}\right)=2\left(\overrightarrow{b}\#\overrightarrow{a}\right)=8(2\hat{i}-2\hat{j}-\hat{k})$

% a unit vector perpendicular to both $\overrightarrow{a}4\overrightarrow{b}$ and $\overrightarrow{a}\overrightarrow{b}$ is

$\frac{8(2\hat{i}-2\hat{j}-\hat{k})}{8\sqrt{441}}=\pm \frac{1}{4}(2\hat{i}-2\hat{j}-\hat{k})$