Question

If $\overrightarrow{a}=\hat{i}+2\hat{j}+\hat{k}$, $\overrightarrow{b}=2\hat{i}+\hat{j}-\hat{k}$, then component of $\overrightarrow{a}$ perpendicular to $\overrightarrow{b}$ is

• A. $\frac{\widehat{5i}}{2}+\frac{\widehat{2i}}{3}+\frac{\hat{k}}{2}$
• B. $\frac{\widehat{5i}}{3}+2\hat{i}+\frac{\hat{k}}{3}$
• C. $\frac{(5\hat{i}+2\hat{i}+\hat{k})}{3}$
• D. $1.5\hat{j}+1.5\hat{k}$

Answer 1

Answer: (D)

$1.5\hat{j}+1.5\hat{k}$

The component of $\overline{a}$ along $\overline{b}$ is $\frac{(\overline{a}.\overline{b})\overline{b}}{|\overline{b}{|}^2}$
So, the component perpendicular to $\overline{b}$ will be $\overline{a}-\frac{(\overline{a}.\overline{b})\overline{b}}{|\overline{b}{|}^2}$

Thus, the component $=(\overline{i}+2\overline{j}+\overline{k})-\frac{3}{6}(2\overline{i}+\overline{j}-\overline{k})=1.5\overline{j}+1.5\overline{k}$