Question

How can planes intersect?

Answer 1

Two planes (in `3` dimensional space) can intersect in one of `3` ways:

• Not at all - if they are parallel.

• In a line.

• In a plane - if they are coincident.

Explanation:

In `3` dimensional Euclidean space, two planes may intersect as follows:

• If one plane is identical to the other except translated by some vector not in the plane, then the two planes do not intersect - they are parallel.

• If the two planes coincide, then they intersect in a plane.

• If neither of the above cases hold, then the planes will intersect in a line.

Note that two planes cannot intersect in one or a finite number of points.