prove that three collinear points can determine a plane.

Question

prove that three collinear points can determine a plane.

Answer 1

A plane in three dimensional space is determined by:

Three NON COLLINEAR POINTS

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.

 

Answer 2

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.