Direction vector ($r=p+td$)

A nonzero vector $d$ is a direction vector of a line if the line has a parametrization $r=p+td$, $t\in \mathbb{R}$, for some point $p$. Replacing $d$ by a nonzero scalar multiple describes the same line; dividing by its Euclidean norm gives a unit vector in one of the two orientations. A cross product of two nonparallel normal vectors supplies a direction vector for the intersection of their planes.