Answer to Question #258 in Geometry for daniel

Question

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.

Answer 1

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.