Find the Unit Tangent For $\vec { r } ( t ) = \left\langle \cos ( 3 t ) , \sin ( 3 t ) , e ^ { t } \right\rangle$

Multiple Choice

Find the unit tangent for $\vec { r } ( t ) = \left\langle \cos ( 3 t ) , \sin ( 3 t ) , e ^ { t } \right\rangle$

A) $\vec { T } ( t ) = \frac { \left\langle - 3 \sin ( 3 t ) , 3 \cos ( 3 t ) , e ^ { t } \right\rangle } { \sqrt { 9 + e ^ { 2 t } } }$
B) $\vec { T } ( t ) = \frac { \left\langle \cos ( 3 t ) , \sin ( 3 t ) , e ^ { t } \right\rangle } { \sqrt { 9 + e ^ { 2 t } } }$
C) $\vec { T } ( t ) = \frac { \left\langle 3 \sin ( 3 t ) , - 3 \cos ( 3 t ) , e ^ { t } \right\rangle } { \sqrt { 9 + e ^ { 2 t } } }$
D) $\vec { T } ( t ) = \left\langle \cos ( 3 t ) , \sin ( 3 t ) , e ^ { t } \right\rangle$