The position vectors of the vertices \( A, B \) and \( C \) 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 \( l \) denotes the length of the angle bisector \( AD \) of \( \angle BAC \) where \( D \) is on the line segment \( BC \), then \( 2l^{2} \) equals:
