Taking the cross product of their normals will give you a vector parallel to the line of intersection, i.e. your direction vector.
Find a position vector that lies on the line of intersection (i.e. that satisfies both equations of the plane). This can be pretty much anything and is why your answer will vary. What you can do is fix a value for x (or y or z) and solve for remaining simpler system of equations for the other 2 variables to get a point common to both planes. This point will form the position vector needed to define your line.