Question

The vector of megnitude $3\sqrt{6}$ along the bcisector of the angle between the vectors $4\overline{i}-7\overline{j}+4\overline{k}$ and $\overline{i}+2\overline{j}-2\overline{k}$ is

• A. $7\overline{i}-\overline{j}-2\overline{k}$
• B. $\pm (7\overline{i}-\overline{j}-2\overline{k})$
• C. $-7\overline{i}-\overline{j}-2\overline{k}$
• D. $\pm (-7\overline{i}-\overline{j}-2\overline{k})$

Answer 1

Answer: (A)

$7\overline{i}-\overline{j}-2\overline{k}$

We have,

$\begin{array}{c}\lambda \left(\frac{4\overline{i}-7\overline{j}+4\overline{k}}{9}+\frac{\overline{i}+2\overline{j}-2\overline{k}}{3}\right)\\ \lambda \left(\frac{7}{9}\overline{i}-\frac{1}{9}\overline{j}-\frac{2}{9}\overline{k}\right)\\ \frac{\sqrt{{\left(7\lambda \right)}^2+{\left(\lambda \right)}^2+4{\lambda }^2}}{9}=3\sqrt{6}\\ \left|\lambda \right|=9\\ \lambda =\pm 9\\ \pm \left(7\overline{i}-\overline{j}-2\overline{k}\right)\end{array}$

Then,

Option $A$ is correct answer.