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

A) $\frac { 27 } { 29 }$
B) $\frac { 10 } { 29 }$
C) $\frac { 50 } { 29 }$
D) $\frac { 7 } { 29 }$