During tutoring (12th grade, regular Math class), I had to explain how to find the two points $s$ and $s'$ that are the base of the perpendicular connection between two skew straight lines $g$ and $h$.
Where $g$ and $h$ are given respectively as: $$ g \colon \mathbb R \to \mathbb R^3; t \mapsto \vec x = \vec x_0 + \vec v_g t $$
What I did is to calculate a normal vector to both $\left(\vec n \propto \vec v_g \times \vec v_h \right)$. Then move $h$ along $\vec n$ so that $h'$ intersects $g$. Then I would just calculate the intersection $s$ of $g$ and $h'$, and move the intersection back down to $h$, yielding $s'$.
Is there any shorter way?