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

Multiple Choice

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 $r ( t ) = \cos 5 t \mathbf { i } + \sin 5 t \mathbf { j } + 4 t \mathbf { k }$ .

A) $\frac { 21 } { 41 }$
B) $\frac { 9 } { 41 }$
C) $\frac { 20 } { 41 }$
D) $\frac { 80 } { 41 }$