Question

The vector component of $\hat{i}+\hat{j}+\hat{k}$ perpendicular to the vector $2\hat{i}-\hat{j}+2\hat{k}$ is

• A. $\frac{\hat{i}+4\hat{j}+\hat{k}}{3}$
• B. $\frac{\hat{i}-4\hat{j}-3\hat{k}}{4}$
• C. $\hat{i}+\hat{j}-\frac{1}{2}\hat{k}$
• D. $\overrightarrow{0}$

Answer 1

The correct option is A $\frac{\hat{i}+4\hat{j}+\hat{k}}{3}$

$\overline{a}=\overline{i}+\overline{j}+\overline{k}\overline{b}=2\overline{i}-2\overline{j}+2\overline{k}\overline{a}\times \overline{b}=\left|\begin{array}{ccc}i& j& k\\ 1& 1& 1\\ 2& -1& 2\end{array}\right|=(2+1)\hat{i}-\hat{j}\left(0\right)+k(-3)=3\hat{i}-\hat{k}componentof\overline{a}\perp larto\overline{b}=\overline{a}-\frac{(\overline{a}-\overline{b})\overline{b}}{{\left(b\right)}^2}=\hat{i}+\hat{j}+\hat{k}-\left[\frac{\left(3\right)(2\hat{i}-j+2\hat{k})}{9}\right]=\frac{\hat{i}+4\hat{j}+\hat{k}}{3}OPTION:A$