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There are two different ways that two planes can interact.
I. Intersecting Planes

Intersecting Planes
Intersecting planes are two planes that meet.
There are two important factors with two intersecting planes:

A) Two planes will intersect in a single line. This line is a line in each plane.

B) There's no way to construct two planes and have them intersect in more than one line.

For a stereographic (or 3D) representation of parallel planes, click here.

II. Parallel Planes
Parallel planes are planes that never meet. Parallel planes always go off in the same direction.
Parallel Planes
Parallel planes always stay equal distance from each other.

For a stereographic (or 3D) representation of parallel planes, click here.

One more point
Given any three intersecting planes, they will intersect in a single point.
Three Intersecting Planes
For a stereographic (or 3D) representation of three intersecting planes, click here.

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