Question

compare collinear points and coplanar points. Are collinear points also coplanar? Are coplanar points also collinear? Explain.

Answer 1

coplanar is only meaningful when it is more than two points. If the set of points are all in the same flat plane, then they are coplanar. Some points which are coplanar are also all in the same line, in which case they are collinear. Not all sets of coplanar points will be collinear.

Answer 2

For example, the set of points in 3D xyz space:
{0,0,0},{1,1,1},{2,2,2},{3,3,3} are collinear.
{0,0,0},{1,1,1},{2,2,2},{3,3,3},{1,-1,1},{2,-2,2},{3,-3,3} are coplanar, but not collinear.

Answer 3

{0,0,0},{1,1,1},{1,1,-1},{1,-1,1},{-1,1,1},{1,-1,-1},{-1,1,-1},{-1,-1,1},{-1,-1,-1} are not coplanar