Let
and
. Assume in turn that each of the intrinsic derivatives of
are some linear combination of the unit vectors
and hence derive the Frenet-Serret formulas of differential geometry.
I am sure thus must be easy but I cannot see it!
If
then taking the dot product of both sides with N and using the first equation given produces
If I claim to know that N is orthogonal to T then I can get the first equation, that is
But when I move onto the next equation
then taking the dot product of both sides with B and using the second equation given produces
.
I cannot see how to get from here to the required equation:
Or the third equation: