University Mathematics Handbook (2015)

III. Analytic Geometry and Vectors

Chapter 5. Plane in Space

5.1  Plane

The equation of plane passing, through point and perpendicular to vector is

Vector is a vector normal to the plane.

5.2  General Form of a Plane Equation

5.3  Distance of a Point to the Plane

The distance of point to plane equals

.

5.4  Parallel Planes

a.  Planes and are parallel to each other if, and only if, their normal vectors and are parallel to each other.

b.  These planes are parallel to each other if, and only if, .

5.5  Angle Between Two Planes

The angle of two non-parallel planes equals to the angle of their normal vectors and or to the supplementary angle of it. Therefore, the cosine of the acute angle between the planes is

Or, in its coordinate form