No , three points will be always coplanar.
Two points are always collinear since there is always a unique line passing through them.2 points are min no. of points needed to determine a line.
Similarly in the case of plane, 3 points are minimum no. of points needed to draw a plane. No matter how you arrange these points , a unique plane will pass through all of them.Therefore , 3 points are always coplanar.
Hope this will help you.