### Plane forms

Point direction form:

where P(x1,y1,z1) lies in the plane, and the direction (a,b,c) is normal to the plane.

General form:

where direction (A,B,C) is normal to the plane.

Intercept form:

this plane passes through the points (a,0,0),(0,b,0) and (0,0,c).

Three point form:

Normal form:

Parametric form:

where the directions (a1,b1,c1) and (a2,b2,c2) are parallel to the plane.

### Angle between two planes:

The angle between planes A1x+B1y+C1z+D1=0 and A2x+B2y+C2z+D2=0 is:

The planes are parallel if and only if

### Equation of a plane

The equation of a plane through P1(x1,y1,z1) and parallel to directions (a1,b1,c1) and
(a2,b2,c2) has an equation:

The equation of a plane through P1(x1,y1,z1) andP1(x2,y2,z2)), and parallel to direction (a,b,c),
has equation

The equation of a plane through P1(x1,y1,z1) , P2(x2,y2,z2) and P3(x3,y3,z3) ,
has equation

### Distance from point to plane

The distance of P1(x1,y1,z1) from the plane Ax+By+Cz+D=0 is

### Intersection of two planes

The intersection of planes A1x+B1y+C1z+D1=0 and A2x+B2y+C2z+D2=0 is the line:

where

If a=b=c=0, then the planes are parallel.