If you know the plane 2x+2y-z-18=0, you know that the normal vector to this plane is 2,2,-1. If you seek know direction vectors of the plane, can you say that (2,2,-1)(x,y,z)=0
2x+2y-z=0 and then invent some points?
Are therefore (1,-1,0),(-1,1,0),(1,1,4) etc. all direction vectors of the plane or am i making some kind of mistake here?