The Torsion of a Curve Defined By $\mathbf { r } ( t )$

Short Answer

The torsion of a curve defined by $\mathbf { r } ( t )$ is given by
$$\tau = \frac { \left( \mathbf { r } ^ { t } \times \mathbf { r } ^ { tt } \right) \cdot \mathbf { r } ^ { ttt } } { \left| \mathbf { r } ^ { t } \times \mathbf { r } ^ { t t } \right| ^ { 2 } }$$
Find the torsion of the curve defined by $\mathbf { r } ( t ) = \cos 2 t \mathbf { i } + \sin 2 t \mathbf { j } + 5 t \mathbf { k }$ .