Vector Algebra

Let \(\mathrm{ABC}\) be a triangle of area \(15 \sqrt{2}\) and the vectors \(\overrightarrow{\mathrm{AB}}=\hat{i}+2 \hat{j}-7 \hat{k}, \overrightarrow{\mathrm{BC}}=\mathrm{a} \hat{i}+\mathrm{b} \hat{j}+\mathrm{c} \hat{k}\) and \(\overrightarrow{\mathrm{AC}}=6 \hat{i}+\mathrm{d} \hat{j}-2 \hat{k}, \mathrm{~d}>0\). Then the square of the length of the largest side of the triangle \(\mathrm{ABC}\) is _________.