Direction vector
= Direction vector
{title2=$r=p+td$}
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>.