let say that gl_Vertex( x,y,z)
and ur modelview matrix is the identity matrix .
so vPosition in eye space will be vPosition(x,y,z,1) in homogeneous form.

so vPosition.z=length( vPosition.xyz ) only if (x=y=0 ) .

yep, could be formulated as finding the values of x, y and z for which x^2 + y^2 + z^2 = z^2, or more simply the x and y for which x^2 = - y^2. None, really.