Line-plane and plane-plane distances

Remark — Line–plane and plane–plane distances

• Parallel planes: $d(\pi_1,\pi_2)$ is the distance of any point of $\pi_1$ from $\pi_2$.
• Line parallel to the plane: $d(r,\pi)$ is the distance of any point of $r$ from $\pi$.
• Line not parallel to the plane: $d = 0$, because the line and the plane intersect.

In every case one reduces to the point–plane distance: it suffices to choose any point on the parallel object.

Links

Topics: Analytic geometry in space
Concepts: Point-plane distance · Plane · Cartesian plane · Line · Line in space
Skills: Analytic geometry · Reasoning by cases