Black box test cases for function which finds intersection of two planes

I'm trying to solve the following task in preperation for Software Engineering exam, but i am stuck.

We want to evaluate a function which finds the intersection of two planes. Input parameter is two vectors, each composed of 3 noncollinear points that define a plane. As a result, the function returns a vector of cross-section, which consists of a minimum number of points to uniquely define the cross-section. In case of an error, the function returns an exception. A point is always represented with integer values for x,y and z coordinate. Suggest test cases to verify correct operation of the function and explain them.

I know I'm supposed to use black box testing and use boundary analysis or equivalence partitions, but i really don't know how to deal with this task other than that. Usually the examples given for these testings are much simpler than this.