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 , called the axis of the pencil.
An improper pencil of planes is the set of the planes parallel to a fixed plane.
Links
Topics: Analytic geometry in space
Concepts: Pencil of planes · Plane
Skills: Analytic geometry