The analogue in space of the pencil of lines in the plane is the pencil of planes. Here too two cases are distinguished.

Definition — Proper and improper pencil

A proper pencil of planes is the set of all the planes that contain a fixed line rr, called the axis of the pencil.

An improper pencil of planes is the set of the planes parallel to a fixed plane.

Topics: Analytic geometry in space
Concepts: Pencil of planes · Plane
Skills: Analytic geometry