Find the Unit Tangent Vector T(t) to the Curve R $\left( t ^ { 2 } - 1,3 t ^ { 2 } - t ^ { 4 } , \frac { 2 } { t } \right)$

question 31

Multiple Choice

Find the unit tangent vector T(t) to the curve r (t) = $\left( t ^ { 2 } - 1,3 t ^ { 2 } - t ^ { 4 } , \frac { 2 } { t } \right)$ when t = 1.

• A) \(\left( \frac { 1 } { \sqrt { 3 } } , \frac { 1 } { \sqrt { 3 } } , - \frac { 1 } { \sqrt { 3 } } \right)\)
• B) \(\left( \frac { 1 } { \sqrt { 3 } } , - \frac { 1 } { \sqrt { 3 } } , - \frac { 1 } { \sqrt { 3 } } \right)\)
• C) \(( 0,1,0)\)
• D) \(( 0,0,1 )\)
• E) \(\left( \frac { 1 } { \sqrt { 3 } } , \frac { 1 } { \sqrt { 3 } } , \frac { 1 } { \sqrt { 3 } } \right)\)
• F) \(\left( \frac { 1 } { \sqrt { 2 } } , 0 , \frac { 1 } { \sqrt { 2 } } \right)\)

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