Set Four
How many planes are determined by a set of four noncoplanar points if no three of the points are collinear?
By guess is one? If some one could help, i would greatly appreciate it! thnx!!
Hint: Think of a pyramid with a triangular base (triangle-based pyramid has 4 vertices)
A line is uniquely determined by two distinct points. The 3D analog is that a plane is uniquely determined by 3 noncollinear points. That being said if we have 4 noncoplanar points no 3 of which are collinear, then to determine how many planes are formed we must count the number of sets of 3 points there are. This is a simple combinations problem (since the order in which we pick the points does not matter). Thus our answer is 4C3 = 4 planes.
You would be right in saying 1 if the four points were coplanar.
90210 – 1×02 “The Jet Set” 1/4 (greek subs)
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