Hello all I have a quick question because I am trying to understand my notes and I am confused. Can anyone here atleast give me a hint or anything!
Taking note of the fact that the normal vector, tangent vector and binormal vector are unit vectors, and form an orthonormal basis. that is, |T|=|N|=|B| and $\lt T , B \gt = 0$, $\lt T , N \gt =0, \lt N , B \gt=0 $
So I know I can write, $ N'=\alpha T + \tau B + \gamma N$, but I want to try to eliminate the N because I know it isn't needed. So, I am trying to do this by taking the inner product of both sides and noting that because N is a unit vector, N' is orthogonal to N for all values.
I am not sure which respect I should take the inner product to, N or N'?
ie, should I do $\lt N',N \gt = \lt \alpha T + \tau B + \gamma N, N \gt$ or N' instead? (and yes I am referring to standard inner product of $\mathbb R^{3} $ Thanks all!