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Since the question is unfinished, I'll assume the most obvious completion: "planes." Yes, a triangular pyramid is composed of 4 non-co-planar points which form 4 intersecting planes.
4 planes.
A cube has 8 non-coplanar points at the vertices and has 6 faces. This is only a partial answer...3 points determine a plane so there will be many more than 6. Your answer is going to be found by the formula n!/(n-r)! where n=8 and r=3. That gives: 40320/120 = 336
Yes, they do.
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Noncoplanar points are points that do not lie on the same plane. If you have two rectangles joined together at points CD, then the rectangle at points ABCD have coplanar points but the points EF are not coplanar, that is, they do not lie on the plane defined by ABCD. On the other hand, the points CDEF are coplanar points but points AB are noncoplanar points. Dr Grips
Noncoplanar is a term in geometry referring two or more figures, lines, or points that do not all lie in the same plane.
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Since the question is unfinished, I'll assume the most obvious completion: "planes." Yes, a triangular pyramid is composed of 4 non-co-planar points which form 4 intersecting planes.
Any three given points can be joined by a common plane, and any two given points can be joined by a common line and an infinite number of common planes.
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4 planes.
A cube has 8 non-coplanar points at the vertices and has 6 faces. This is only a partial answer...3 points determine a plane so there will be many more than 6. Your answer is going to be found by the formula n!/(n-r)! where n=8 and r=3. That gives: 40320/120 = 336
No, A plane can be drawn through any 3 points. If the 3 points are collinear then they make a line and a plane can contain a line. If the points are noncollinear then they can be used to form the corners of a triangle; all points of a triangle are in the same plane.
Coplanarity is equivalent to the statement that the pair of lines determined by the four points are not skew, and can be equivalently stated in vector form as