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Math formulas: Planes in three dimensions

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Plane forms

Point direction form:

where lies in the plane, and the direction is normal to the plane.

General form:

where direction is normal to the plane.

Intercept form:

this plane passes through the points and .

Three point form:

Normal form:

Parametric form:

where the directions and are parallel to the plane.

Angle between two planes:

The angle between planes and is:

The planes are parallel if and only if

Equation of a plane

The equation of a plane through and parallel to directions and has an equation:

The equation of a plane through and), and parallel to direction , has equation

The equation of a plane through , and , has equation

Distance from point to plane

The distance of from the plane is

Intersection of two planes

The intersection of planes and is the line:

where

If , then the planes are parallel.

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