Find the Unit Tangent Vector of the Given Curve $$r ( t ) = ( 2 \cos 6 t ) i + ( 2 \sin 6 t ) j - 5 t k$$

Multiple Choice

Find the unit tangent vector of the given curve.
- $$r ( t ) = ( 2 \cos 6 t ) i + ( 2 \sin 6 t ) j - 5 t k$$

A) $\mathbf { T } = \left( - \frac { 12 } { 13 } \sin 6 \mathrm { t } \right) \mathbf { i } + \left( \frac { 12 } { 13 } \cos 6 \mathrm { t } \right) \mathbf { j } - \frac { 5 } { 13 } \mathbf { k }$
B) $T = \left( - \frac { 12 } { 13 } \cos 6 t \right) i + \left( \frac { 12 } { 13 } \sin 6 t \right) j - \frac { 5 } { 13 } \mathbf { k }$
C) $\mathrm { T } = \left( - \frac { 12 } { 169 } \cos 6 \mathrm { t } \right) \mathrm { i } + \left( \frac { 12 } { 169 } \sin 6 \mathrm { t } \right) \mathrm { j } - \frac { 5 } { 169 } \mathbf { k }$
D) $T = \left( - \frac { 2 } { 13 } \sin 6 t \right) i + \left( \frac { 2 } { 13 } \cos 6 t \right) j - \frac { 5 } { 13 } \mathbf { k }$