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Infinitely many planes contain any two given points- it takes three (non-collinear) points to determine a plane.
Three or more points are collinear if they are all in the same straight line. They are non collinear if at least one of them is not on the same line as the rest. Four or more points are coplanar if they are all in the same plane. They are non coplanar if at least one of them is not on the same plane as the rest.
Three non-collinear points always define exactly one and only one plane. That's why a 3-legged table or chair never wobbles.
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.
Collinear points are points that lie on the same line, while coplanar points are points that lie on the same plane.