Two planes intersect to always form a line.
How do two planes intersect?
In three 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.
We can not find a unique solution for the intersection of two planes. But using substitution or elimination method, we can get it to an equation of two variables (which is a line) which cannot be solved uniquely for one variable individually.
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