Find the Unit Tangent Vector for the Curve Given By \mathbf

Find the unit tangent vector for the curve given by $\mathbf { r } ( t ) = \left\langle \frac { 1 } { 7 } t ^ { 7 } , \frac { 1 } { 3 } t ^ { 3 } , t \right\rangle$ .

A) $\frac { \left\langle t ^ { 6 } , t ^ { 2 } , 1 \right\rangle } { \sqrt { t ^ { 10 } + t ^ { 4 } } }$
B) $\frac { \left\langle t ^ { 6 } , t ^ { 2 } , 1 \right\rangle } { \sqrt { 6 t ^ { 12 } + 4 t ^ { 4 } + 1 } }$
C) $\frac { \left\langle t ^ { 6 } , t ^ { 2 } , 1 \right\rangle } { \sqrt { t ^ { 12 } + t ^ { 4 } } }$
D) $\frac { \left\langle t ^ { 6 } , t ^ { 2 } , 1 \right\rangle } { \sqrt { t ^ { 12 } + t ^ { 4 } + 1 } }$
E) None of these

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