Take two lines given by their equations and I want to know if they are coplanar. If they are either intersecting or parallel, is it enough to conclude that they are coplanar?
2026-03-26 04:21:27.1774498887
Affine geometry, coplanar lines
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Yes, that is indeed sufficient. We prove that this is true as follows:
If the lines are intersecting or parallel, it is clear that they are planar. Now suppose that two lines are coplanar. Then two lines in the same plane must intersect unless they are parallel, so this proves the reverse direction. So we conclude that the given conditions are sufficient and necessary.