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 ++1 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
2
A
2
B
2
C
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)