planes in R³

Summary

Vector equation of a plane

• represents any point on the plane

Normal vector using cross product

Cartesian equation of a plane

Concept

Normal is perpendicular to the plane, perpendicular rule of dot product

Acute angle between line and plane

• due to being perpendicular to the plane

Acute angle between planes

Line of intersection of 2 planes

Direction vector is perpendicular to both normals

Application

Equation of plane from 2 parallel vectors and a point

Intersection between line and plane

Intersection between 2 planes

Extra