Shortest distance between skew lines ($d=|\Delta a\cdot (m_1\times m_2)|/|m_1\times m_2|$)

For lines $a_1+t{m}_1$ and $a_2+u{m}_2$ with nonparallel direction vectors, their shortest separation is the absolute orthogonal projection of $a_2-a_1$ onto their common normal $m_1\times m_2$. Components in the span of $m_1,m_2$ can be cancelled by choosing $t,u$, while the normal component cannot. The same formula gives zero for intersecting nonparallel lines. Parallel lines instead have separation $|(a_2-a_1)\times m_1|/|m_1|$.