Distance Between a Point and a Plane

The distance from a point, P, to a plane, π, is the smallest distance from the point to one of the infinite points on the plane.

This distance corresponds to the perpendicular line from the point to the plane.

Distance between a Point and a Plane

Distance between a Point and a Plane Formula


Examples

Calculate the distance from Point P = (3, 1, −2) to the planes Distance Between a Point and a Plane Example and Distance Between a Point and a Plane Example.

Point and a Plane Operations

Point and a Plane Distance

Calculate the distance from Point Q = (5, 5, 3) to the plane Distance Between a Point and a Plane Example.

Point and a Plane

Point and a Plane Distance


Distance Between Parallel Planes

The distance between two parallel planes is the distance from any point from one plane to a point on the other plane.

It is also possible to calculate the distance using this form:

Distance Between Parallel Planes Example

Distance Between Parallel Planes Solution


Example

Calculate the distance between the planes Distance Between Parallel Planes Example and Distance Between Parallel Planes Example.

Proportions

The two planes are parallel.

Transform the equation of the second plane so that the two planes have the same normal vector.

Parallel Plane Operations

Distance Between Parallel Planes Solution