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prove that three collinear points can determine a plane.

prove that three collinear points can determine a plane.
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2 Answers

A plane in three dimensional space is determined by:
Two non parallel vectors and their intersection.
A point P and a vector to the plane.
So I can't prove that in analytic geometry.


I think the answer of Francisco is very good. However, I might phrase it a little differently --
  • three noncollinear points determine a unique plane - that is, one and only one plane
  • three collinear points determine an infinite number of planes -- that is, many planes can pass through the same line.
Thank you guys I appreciate your additions.
3 collinear points, which by def'n lie along a line, do not sufficiently determine a (unique) plane in Euclidean space.  Infinitely many planes contain a given line.