Suppose that the three coordinate planes are all mirrored and a light ray given by vector a=(a1,a2,a3) first strikes the xz-plane, then the reflected...

Suppose that the three coordinate planes are all mirrored and a light ray given by vector a=(a1,a2,a3) first strikes the xz-plane, then the reflected ray strikes the xy-plane and the reflected ray of this ray strikes the yz-plane. Use the fact that angle of incidence equals the angle of reflection, show that the reflected ray b=(a1,-a2,a3). Deduce that after being reflected by all three mutually perpendicular mirrors, the resulting ray is parallel to the initial ray. Thank you.