Let ABC be a triangle of area 15 √ 2 and the vectors AB = i +2 j -7 k, BC = a i + b j + c k and A C =6 i +d j -2 k, d>0. Then the square of the…

Let ABC be a triangle of area $\displaystyle 15 \sqrt{2}$ and the vectors $\displaystyle \overrightarrow{\mathrm{AB}}=\hat{i}+2 \hat{j}-7 \hat{k}, \overrightarrow{\mathrm{BC}}=\mathrm{a} \hat{i}+\mathrm{b} \hat{j}+\mathrm{c} \hat{k}$ and $\displaystyle \overrightarrow{A C}=6 \hat{i}+d \hat{j}-2 \hat{k}, d>0$. Then the square of the length of the largest side of the triangle $\displaystyle A B C$ is $\displaystyle \_\_\_\_$.