Lemma (Unit Normal)         [Graphics:Images/CurvatureMod_gr_22.gif].

Verification.

Recall.  Two vectors are perpendicular if and only if their dot product is zero.

    It is easy to verify that  [Graphics:../Images/CurvatureMod_gr_23.gif]  is perpendicular to  [Graphics:../Images/CurvatureMod_gr_24.gif]  with the calculation  

[Graphics:../Images/CurvatureMod_gr_25.gif].  

It is also possible to have Mathematica verify this computation.

[Graphics:../Images/CurvatureMod_gr_26.gif]

 

 

 

[Graphics:../Images/CurvatureMod_gr_27.gif]

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

 

(c) John H. Mathews 2004