The position vectors of the vertices $A,B,C$ of a triangle are $2\hat i-3\hat j+3\hat k$, $2\hat i+2\hat j+3\hat k$ and $-\hat i+\hat j+3\hat k$ respectively. Let $l$ denote the length of the angle bisector $AD$ of $\angle BAC$ (where $D$ is on the line segment $BC$). Then $2l^{2}$ equals: