The derivative of the Tangent vector $T$ is orthogonal to the tangent vector. The norm of this vector $k=|T'|$ is the curvature of the curve at the point (Curvature of a curve)

The normal vector is the normalized version of this vector $N=T'/k$.

To complete the basis we introduce the binormal vector $B=T \times N$. The magnitude of the derivative of the binormial vector defines the torsion (Torsion of a curve). One can then derive Frenet formulae