From Exercise 16 (e) in Chapter 1: Given a line m not parallel to 
the picture plane omega, the vanishing point V_m is defined to be
the intersection of the picture plane omega with the line through
the artist's eye/nose that is parallel to m.  

Note that this definition excludes the possibility that m is parallel
to the picture plane, so the vanishing point is not defined in this case.
However, if we apply the rest of the definition anyway, we see that 
any line parallel to m is parallel to the plane omega, so does not 
intersect it, hence there is no vanishing point V_m.