Line-plane intersection criterion
= Line-plane intersection criterion
A line $r=b+s m$ intersects a plane $(r-a)\cdot n=0$ exactly when the scalar equation $s(m\cdot n)=(a-b)\cdot n$ can be solved. If $m\cdot n\ne0$, there is one point. If that product vanishes, the line is either contained in the plane or disjoint from it. Direction and normal vectors must be nonzero.