the cross product is always orthogonal/perpendicular or 90 degrees from the 2 vectors it forms right?
so like if you had the unit vectors for the x axis and the y axis and you took their cross products you'd get:
(1,0,0) x (0,1,0) = (0,0,1)
So if you took that with the cross product of the other say the x axis you should get something perpendicular to both the x axis and the z axis, which is the y axis.
Does that help any?