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A set of three points not on the same line are points that define a unique plane.more than three points not on a plane are in a space (volume).
Three balls on a table are three coplanar points.
To find a point equidistant from three other points, construct perpendicular bisectors for two of the segments formed from three points. Note: this will be the center of the circle that has all three points on it's circumference. Three points, not in a straight line, form three pairs of points with each pair defining a different line. Take any pair of points and draw the perpendicular bisector of the line joining them. Repeat for one of the other pairs. These two perpendicular bisectors will meet at the point which is equidistant from all three points - the circumcenter of the triangle formed by the three points.
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In 3-dimensional space, yes, any three points are coplanar.