The position vector of the vertices $A,B,C$ of a $\Delta\: ABC$ are $\hat i-\hat j-3\hat k,\:2\hat i+\hat j-2\hat k\:\:and\:\:-5\hat i+2\hat j-6\hat k$ respectively. The length of the bisector $AD$ of angle $A$ where $D$ is on the line $BC$ is ?

Question

$\begin{array}{1 1} \large (a)\:\frac{15}{2}\;\:\:\qquad\:\:(b)\:\:\frac{11}{2}\:\:\:\qquad\:\:(c)\:\:\frac{1}{4}\:\:\:\qquad\:\:(d)\:\:\frac{3}{4} \sqrt {10} \end{array} $