Do 3 noncollinear points have to be coplanar?

Question

If you have a rectangular prism and the points are the vertices, when picking noncollinear points, do they have to be on the same plane?

Answer 1

Here is an intuitive way to look at it:

 

Connect any 2 of the 3 points, forming an axis of rotation.  Now consider a plane that intersects the rotation axis, with the axis lying in the plane.  Rotate the plane in any direction around the axis until it touches the 3rd point.  Then all 3 points lie in the rotated plane, and hence are coplanar.  You can think of them as corners of a triangle lying in the plane.  In short, any 3 points will necessarily be coplanar even when not colinear.  But as the tutors pointed out, that plane might not coincide with a surface of the prism in the problem.

Answer 2

If these three points are noncollinear, there will be exactly one plane that 

all three of them lie on.   They will be coplanar by definition.  You don't even

have to try to see to it they lie on the same plane, they will by definition!

 

With that said, the plane that all three points  lie on may not be one

of the sides of the rectangular prism.

Answer 3

Three noncollinear points do not have to be coplanar, i.e., they do not have to be in the plane under discussion, yet three noncollinear points do define a plane.