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

question 39

Multiple Choice

Find the unit tangent vector for the curve given by $\mathbf { r } ( t ) = \left\langle \frac { 1 } { 5 } t ^ { 5 } , \frac { 1 } { 3 } t ^ { 3 } , t \right\rangle$ .

• A) \(\frac { \left\langle t ^ { 4 } , t ^ { 2 } , 1 \right\} } { \sqrt { t ^ { 10 } + t ^ { 4 } } }\)
• B) \(\frac { \left\langle t ^ { 4 } , t ^ { 2 } , 1 \right) } { \sqrt { 4 t ^ { 8 } + 4 t ^ { 4 } + 1 } }\)
• C)
• \(\frac { \left\langle t ^ { 4 } , t ^ { 2 } , 1 \right) } { \sqrt { t ^ { 8 } + t ^ { 4 } + 1 } }\)
• D)
• \(\frac { \left\langle t ^ { 4 } , t ^ { 2 } , 1 \right\rangle } { \sqrt { t ^ { 8 } + t ^ { 4 } } }\)
• E) None of these