Assume you are given the number of points k that are known to be coplanar with each other, but there are a total of n points given. How do you determine which points are the coplanar points? To give a more specific context, I'm working with k = 4 and n = 6 in 3D space (x,y,z).
I know that you can determine whether or not 4 points are coplanar using either the Scalar Triple Product or finding the determinant of their matrix, but to my knowledge, neither of those would necessarily work unless I were testing whether or not ALL points were coplanar. What can be done in the case where only a certain number of the points are coplanar and need to be found?
You could just create multiple plane equations and test for whether or not the points are within each, until you eventually get the plane equation which has exactly 1 other point contained in it, but I am curious if there are any better work-arounds using linear algebra or multivariable calculus.