Equation of a Plane

Parametric equations

let be a normal vector to the plane containing
let be any point on the plane

Consider a non-vertical plane passing through the point , with . These are vertical extensions of lines in the xy-plane, so their equations are .

• Let be another plane, and consider the vector . It will lie in the plane as well.
• Let but a normal vector to the plane.

These two vectors must be perpendicular, that is, (see dot product), which gives

If we take , and then set and , we obtain:

so an alternate equation to our plane is