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: