In what ways can two planes intersect?
1 Answer
Typically two planes intersect along some line. If the planes happen to be parallel, then they will either not intersect at all or they will be the same plane.
Explanation:
If the equations of the two planes are given, and the left-hand sides of the equations are not multiples of each other (when written in standard form), then the planes will intersect along some line. The solution set of such a system (the intersection line) is typically represented in parametric form.
For example, if the equations are
If you rewrite this system with
The solution line therefore goes through the point