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Can two planes that do not intersect be parallel?
No. By definition, planes can be extended in all directions to infinity. If they are not parallel, they will intersect somewhere.
Do two planes intersect in infinitely many points?
No, perpendicular planes intercept at only one point. Parallel planes do not intersect at all.
What is the intersection of two planes?
If there are two unique, non-parallel planes in space, they will intersect, and their intersection will be a line.
If two planes intersect what is their intersection called?
A line. When two planes intersect, their intersection is a line.
Can two different planes intersect a line?
Yes, there are three ways that two different planes can intersect a line: 1) Both planes intersect each other, and their intersection forms the line in the system. This system's solution will be infinite and be the line. 2) Both planes intersect the line at two different points. This system is inconsistent, and there is no solution to this system. However, both planes will still be intersecting the same line, albeit at different locations on the line. 3) Both planes intersect each other, but their intersection does NOT form the line in the system. However, if the line in the system intersects the planes' intersection, then they will all intersect a single point. The solution will be finite and be a single point. There are also 3 ways two different planes WON'T both intersect a line. 1) The two planes and the line are all parallel to each other, and none of them intersect each other. 2) The line is parallel to one plane, but intersects the other plane. 3) The same as #2, but now the line is parallel to the other plane and intersects the one plane.
