If you have a plane parallel to XY reference frame (Z=a) , the line connecting the two points (p1 and p2) will cross the plane if the z component of the vector of that line (v=p2-p1) is nonzero, a.k.a not parallel to the plane.
%Orthogonal case
p1=[1 3 4];
p2=[5 6 8];
v=p2-p1;
v(3)==0 %If 0 it crosses the plane otherwise the plane and the line are parallel to each other
%Parallel case
p1=[1 3 4];
p2=[5 6 4];
v=p2-p1;
v(3)==0 %If 0 it crosses the plane otherwise the plane and the line are parallel to each other
