Let the position vectors of the vertices $A, B$ and $C$ of a triangle be $2 \hat{\imath}+2 \hat{\jmath}+\hat{k}, \hat{\imath}+2 \hat{\jmath}+2 \hat{k}$ and $2 \hat{\imath}+\hat{\jmath}+2 \hat{k}$ respectively. Let $l_1, l_2$ and $l_3$ be the lengths of perpendiculars drawn from the ortho center of the triangle on the sides $\mathrm{AB}, \mathrm{BC}$ and CA respectively, then $l_1^2+l_2^2+l_3^2$ equals :