Shortest distance between parallel lines

Consider the following parallel lines.

$L_1 : \tvec{r}_1 = \tvec{i} + 3\tvec{j} + \tvec{k} + s\left(\tvec{i} + \tvec{j} + \tvec{k}\right)$ and $L_2 : \tvec{r}_2 = -2\tvec{i} + \tvec{j} + 3\tvec{k} + t\left(\tvec{i} + \tvec{j} + \tvec{k}\right)$ where $s, t \in R$.

The shortest distance between $L_1$ and $L_2$ is