The lines $\vec{r} = \vec{a}_1 + \lambda\vec{b}$ and $\vec{r} = \vec{a}_2 + \mu\vec{b}$ are parallel and distinct. Which expression gives the distance between them?

Explanation

1. 01

   For parallel lines $\vec{b} \times \vec{b} = \vec{0}$, so the skew-lines formula would divide by 0.

2. 02

   The gap is the part of $\vec{a}_2 - \vec{a}_1$ across $\vec{b}$: $d = \frac{\lvert \vec{b} \times (\vec{a}_2 - \vec{a}_1) \rvert}{\lvert \vec{b} \rvert}$.