Let the three sides of a triangle ABC be given by the vectors 2 i - j + k, i -3 j -5 k and 3 i -4 j -4 k. Let G be the centroid of the triangle ABC.…

Let the three sides of a triangle ABC be given by the vectors $\displaystyle 2 \hat{i}-\hat{j}+\hat{k}, \hat{i}-3 \hat{j}-5 \hat{k}$ and $\displaystyle 3 \hat{i}-4 \hat{j}-4 \hat{k}$. Let G be the centroid of the triangle ABC . Then $\displaystyle 6\left(|\overrightarrow{\mathrm{AG}}|^2+|\overrightarrow{\mathrm{BG}}|^2+|\overrightarrow{\mathrm{CG}}|^2\right)$ is equal to $\displaystyle \_\_\_\_$.