Tangent vector cross product with binormal vector

Question

If $\gamma$ is a curve in space with unit tangent, unit normal and binormal $T,N,B$ respectively, is it true that \begin{equation} T \times B =-N \end{equation} ? I feel that this should be true by analogy with the canonical basis for $\mathbb{R}^3$.

Answer 1

Using circular shift property of cross product we get: $$\langle T \times B,N \rangle=\langle N \times T,B \rangle=-\langle T \times N,B \rangle=-1$$