Prove. The normal N to surface S at point (r, s) — which corresponds to point P on C — is parallel to the binormal B of curve C at P.
Proof. The equation of the tangent surface S of curve C is given by
The normal to S at point (r, s) is given by so we now compute it. Taking derivatives of 1) we get
where is the principal normal to curve C at point P. Thus
Since and we have
where is the binormal to C at P. Thus the normal is a multiple of