question_answer

The vector \[\vec{c}\]directed along the internal bisector of the angle between the vectors  \[\vec{a}=7\hat{i}-4\hat{j}-4\hat{k}\]and \[\vec{b}=-2\hat{i}-2\hat{j}+2\hat{k}\]with \[|\vec{c}|=5\sqrt{6}\]is

A)  \[\pm \frac{5}{2}(\hat{i}-7\hat{j}+2\hat{k})\]

B)  \[\frac{5}{2}(5\hat{i}+5\hat{j}+2\hat{k})\]

C)  \[\frac{5}{2}(\hat{i}+7\hat{j}+2\hat{k})\]

D)  \[\frac{5}{2}(-5\hat{i}+5\hat{j}+2\hat{k})\]