Prove that if through three given points two planes can be drawn, then infinitely many planes through these points can be drawn. I don't get how this is possible, since there is unique plane passing through three point, how would I get two planes?
[Math] Prove that if through three given points two planes can be drawn, then infinitely many planes throught these points can be drawn.
3dgeometry
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Best Answer
Beware the hidden assumption."There is a unique plane passing through 3 points." This is only true if the 3 points are not co-linear. Don't assume the points are NOT co-linear. If 2 planes intersect, their intersection is a line, and there are infinitely planes containing that line. So if 3 points are co-linear, there are infinitely many planes through the line that contains the 3 points.