If $\overline{\mathrm{OA}} = 2\overline{\mathrm{i}} + 2\overline{\mathrm{J}} + \overline{\mathrm{k}}, \overline{\mathrm{OB}} = 2\overline{\mathrm{i}} + 4\overline{ \mathrm{j}} + 4\overline{\mathrm{k}}$

 and the length of the internal bisector of $\angle$BOA of triangle AOB is k, then $9{\mathrm{k}}^2=$