Let $l_1$ be the line passing through the point $3 \bar{i}+4 \bar{j}-2 \bar{k}$ and parallel to the vector $-\bar{i}+2 \bar{j}+\bar{k}$. Let $l_2$ be another line passing through the point $\bar{i}-7 \bar{j}-2 \bar{k}$ and parallel to the vector $\bar{i}+3 \bar{j}+2 \bar{k}$. Then the shortest distance between the lines $l_1$ and $l_2$ is