Q: Why four points may or may not be coplanar?

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3 coplanar points may or may not be collinear. 3 collinear points must be coplanar.

all of them are collinear they lie in the same plane

No. If the four points are coplanar, they determine only one plane!

They need not be. The four vertices of a quadrilateral are coplanar but NOT collinear. On the other hand, any line (in Eucledian geometry) has an infinite number of points on it - all of which are coplanar.

Three points are, but not four.

No. A trinagle does not require four points, three are sufficient. And any three points, if they are not colinear, must be coplanar.

No, they always are From Wikipedia.org, "The World's Encyclopedia" when I searched coplanar In geometry, a set of points in space is coplanar if the points all lie in the same geometric plane. For example, three distinct points are always coplanar; but four points in space are usually not coplanar. Since 3 points are always coplanar. A point and line are always coplanar

Yes, they are.

Yes, they are.

space

not necassarily

life