Question

The vector $\overrightarrow{c}$ along the bisector of angle between $\overrightarrow{a}=7\hat{i}-4\hat{j}-4\hat{k}$ and $\overrightarrow{b}=-2\hat{i}-\hat{j}+2\hat{k},$ where $|\overrightarrow{c}|=\sqrt{270},$ is given by

• A. $\sqrt{5}(\hat{i}-7\hat{j}+2\hat{k})$
• B. $-13\hat{i}+\hat{j}+10\hat{k}$
• C. $-\hat{i}+7\hat{j}+2\hat{k}$
• D. $\hat{i}-7\hat{j}-2\hat{k}$

Answer 1

The correct option is A $\sqrt{5}(\hat{i}-7\hat{j}+2\hat{k})$

$\overrightarrow{a}=7\hat{i}-4\hat{j}-4\hat{k},\overrightarrow{b}=-2\hat{i}-\hat{j}+2\hat{k},\overrightarrow{c}=\lambda (\hat{a}+\hat{b})\Rightarrow \overrightarrow{c}=\sqrt{270}\left(\frac{\hat{a}+\hat{b}}{|\hat{a}+\hat{b}|}\right)\Rightarrow \overrightarrow{c}=\sqrt{5}(\hat{i}-7\hat{j}+2\hat{k})$