Find the unit tangent vector T(t) to the curve r (t) = $\left( \sin t , 2 t , t ^ { 2 } \right)$ when t = 0.
A) $\left( - \frac { 2 } { \sqrt { 5 } } , - \frac { 1 } { \sqrt { 5 } } , 0 \right)$

B) $\left( \frac { 2 } { \sqrt { 5 } } , - \frac { 1 } { \sqrt { 5 } } , 0 \right)$
C) $\left( - \frac { 2 } { \sqrt { 5 } } , \frac { 1 } { \sqrt { 5 } } , 0 \right)$
D) $\left( \frac { 2 } { \sqrt { 5 } } , \frac { 1 } { \sqrt { 5 } } , 0 \right)$
E) $\left( - \frac { 1 } { \sqrt { 5 } } , - \frac { 2 } { \sqrt { 5 } } , 0 \right)$
F) $\left( \frac { 1 } { \sqrt { 5 } } , - \frac { 2 } { \sqrt { 5 } } , 0 \right)$

G) $\left( - \frac { 1 } { \sqrt { 5 } } , \frac { 2 } { \sqrt { 5 } } , 0 \right)$

H) $\left( \frac { 1 } { \sqrt { 5 } } , \frac { 2 } { \sqrt { 5 } } , 0 \right)$

Question

Find the unit tangent vector T(t) to the curve r (t) = $\left( \sin t , 2 t , t ^ { 2 } \right)$ when t = 0.
A) $\left( - \frac { 2 } { \sqrt { 5 } } , - \frac { 1 } { \sqrt { 5 } } , 0 \right)$

B) $\left( \frac { 2 } { \sqrt { 5 } } , - \frac { 1 } { \sqrt { 5 } } , 0 \right)$ 
C) $\left( - \frac { 2 } { \sqrt { 5 } } , \frac { 1 } { \sqrt { 5 } } , 0 \right)$ 
D) $\left( \frac { 2 } { \sqrt { 5 } } , \frac { 1 } { \sqrt { 5 } } , 0 \right)$ 
E) $\left( - \frac { 1 } { \sqrt { 5 } } , - \frac { 2 } { \sqrt { 5 } } , 0 \right)$ 
F) $\left( \frac { 1 } { \sqrt { 5 } } , - \frac { 2 } { \sqrt { 5 } } , 0 \right)$

G) $\left( - \frac { 1 } { \sqrt { 5 } } , \frac { 2 } { \sqrt { 5 } } , 0 \right)$

H) $\left( \frac { 1 } { \sqrt { 5 } } , \frac { 2 } { \sqrt { 5 } } , 0 \right)$

Quizplus · Accepted Answer

The derivative of r(t) is r'(t) = (cos(t), 2, 2t). At t = 0, r'(0) = (1, 2, 0). The magnitude of r'(0) is √(1^2 + 2^2 + 0^2) = √5. The unit tangent vector T(t) is r'(t) / |r'(t)|, so T(0) = (1/√5, 2/√5, 0).

Find the Unit Tangent Vector T(t) to the Curve R (sin⁡t,2t,t2)\left( \sin t , 2 t , t ^ { 2 } \right)(sint,2t,t2)

Find the Unit Tangent Vector T(t) to the Curve R $\left( \sin t , 2 t , t ^ { 2 } \right)$