Consider the Three Point Postulate. Also, consider intersecting planes.
Different planes: The three points are collinear. Same plane: The three points cannot be collinear.
Practice makes perfect
The Three Point Postulate tells us that through any three noncollinear points there exists exactly one plane. Therefore, if plane P contains three noncollinear points, there is no way we can draw a second plane through these points that isn't identical to P. We show an example of this below.
If we are going to be able to draw a completely new plane containing all of the points, they would have to be collinear like below.
Now we can draw a plane Q that intersects plane P at the line that contains our points.
Consequently, if we want to force P and Q to coincide, the three points cannot be collinear. We showed this in the beginning of the solution.
