Let l_1 be the line in x y -plane with x and y intercepts 1/8 and 1/(4 √ 2) respectively, and l_2 be the line in z x -plane with x and z intercepts…

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