Answer to Question #258 in Geometry for daniel

Question #258
There are four points, which don’t belong to the same plane. Can any three of these points belong to the same straight line? Explain your answer.
1
Expert's answer
2010-06-08T07:32:54-0400
No, they can’t. Suppose that three points A, B and C belong to the same line called l. Consider three points: A, B and D. We can build the plane, which contains these 3 points, and there is one such plane only. This plan contains points A and B, so it contains the line l and thus it contains the point C. We get all four points belong to the same plane. So, we get the contravention.

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