# Three Points Determine a Plane

Three Points Determine a Plane

Three noncollinear points in three dimensions determine a unique plane with an equation of the form , where and is the positive distance of the plane from the origin. The vector is normal (perpendicular) to the plane and has norm (length) equal to 1.

Ax+By+Cz=D

A+B+C1

2

2

2

D

(A,B,C)

For such an equation, the signed distance from a point to the plane is given by . Points on the same side of the plane have the same sign.

(x,y,z)

(A,B,C,D)·(x,y,z,-1)