Planes

Equation of planes can expressed in either vector or cartesian form. Vector equation is the one containing only vectors. Cartesian equation is in the form: .

Contains a point and parallel to 2 vectors

Suppose a plane:

• is parallel to both and where
• contains

Equation for the plane is:

Contains a point and normal is given

Suppose a plane:

• contains
• has a normal

Equation for the plane is:

Contains 3 points

Suppose a plane contains ( are the position vectors of respectively).

Normal to a plane

Suppose is a plane. is a normal to the plane.

Angle between 2 planes

Consider the two planes:

The angle between the planes is given by:

Here are normal to the planes .

Shortest distance to a point

Considering a plane .

• is a normal to the plane
• is the position vector of any known point on the plane
• is the position vector to the arbitrary point