Let $l_1$ be the line in xy - plane with x and y intercepts $\frac{1}{8}$ and $\frac{1}{4 \sqrt{2}}$ respectively, and $l_2$ be the line in zx - plane with $x$ and $z$ intercepts $-\frac{1}{8}$ and $-\frac{1}{6 \sqrt{3}}$ respectively. If $d$ is the shortest distance between the line $l_1$ and $l_2$, then $\mathrm{d}^{-2}$ is equal to