The vector $\overset{⇀}{c}$ directed along the internal bisector of the angle between the vectors $2 \bar{i} + 3 \bar{j} - 6 \bar{k}$ and $- 2 \bar{i} - \bar{j} + 2 \bar{k}$ with $| \bar{c} | = 10 \sqrt{21}$ is

see full answer

Your Exam Success, Personally Taken Care Of

1:1 expert mentors customize learning to your strength and weaknesses – so you score higher in school , IIT JEE and NEET entrance exams.

An Intiative by Sri Chaitanya

$10 (- 4 \bar{i} + \bar{j} - 2 \bar{k})$

$(- 8 \bar{i} + 2 \bar{j} - 4 \bar{k})$

$(- 12 \bar{i} + 3 \bar{j} - 6 \bar{k})$

$(12 \bar{i} + 3 \bar{j} + 6 \bar{k})$

answer is B.

(Unlock A.I Detailed Solution for FREE)

Best Courses for You

JEE

NEET

Foundation JEE

Foundation NEET

CBSE

Detailed Solution

$\begin{array}{rcl} 10 \sqrt{21} (\frac{\hat{a} + \hat{b}}{| \hat{a} + \hat{b} |}) & = & 10 \sqrt{21} (\frac{\frac{2 \hat{i} + 3 \hat{j} - 6 \hat{k}}{7} + \frac{- 2 \hat{i} - \hat{j} + 2 \hat{k}}{3}}{|\frac{2 \hat{i} + 3 \hat{j} - 6 \hat{k}}{7} + \frac{- 2 \hat{i} - \hat{j} + 2 \hat{k}}{3}|}) \\ = & 10 \sqrt{21} (\frac{6 \hat{i} + 9 \hat{j} - 18 \hat{k} - 14 \hat{i} - 7 \hat{j} + 14 \hat{k}}{|6 \hat{i} + 9 \hat{j} - 18 \hat{k} - 14 \hat{i} - 7 \hat{j} + 14 \hat{k}|}) \\ = & 10 \sqrt{21} (\frac{- 8 \hat{i} + 2 \hat{j} - 4 \hat{k}}{2 \sqrt{21}}) \\ = & 10 (- 4 \hat{i} + \hat{j} - 2 \hat{k}) \end{array}$ =