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

question 46

Multiple Choice

Find the unit tangent vector to the curve r (t) = $\left\{ e ^ { 2 t } \cos t , e ^ { 2 t } \sin t , e ^ { 2 t } \right\}$ at the point where t = $\frac { \pi } { 2 }$ .

• A) \(\left( \frac { 2 } { 3 } , - \frac { 2 } { 3 } , \frac { 1 } { 3 } \right)\)
• B) \(\left( \frac { 2 } { 3 } , - \frac { 1 } { 3 } , \frac { 2 } { 3 } \right)\)
• C) \(\left( - \frac { 1 } { 3 } , \frac { 2 } { 3 } , \frac { 2 } { 3 } \right)\)
• D) \(\left( \frac { 2 } { 3 } , \frac { 2 } { 3 } , - \frac { 1 } { 3 } \right)\)
• E) \(\left( \frac { 3 } { \sqrt { 14 } } , \frac { 2 } { \sqrt { 14 } } , - \frac { 1 } { \sqrt { 14 } } \right)\)
• F) \(\left( - \frac { 2 } { \sqrt { 14 } } , \frac { 1 } { \sqrt { 14 } } , \frac { 3 } { \sqrt { 14 } } \right)\)
• G) \(\left( \frac { 1 } { \sqrt { 14 } } , - \frac { 3 } { \sqrt { 14 } } , \frac { 2 } { \sqrt { 14 } } \right)\)
• H) \(\left( \frac { 1 } { \sqrt { 6 } } , \frac { 2 } { \sqrt { 6 } } , \frac { 1 } { \sqrt { 6 } } \right)\)

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Definitions:

Cerebrum

The largest part of the brain. It is divided into two hemispheres with four lobes in each hemisphere.

Midbrain

That portion of the brain connecting the pons and the cerebellum.

Thalamus

A portion of the brain lying between the cerebrum and the midbrain.

Spinal Nerves

Bundles of motor and sensory nerves that connect the central nervous system to the rest of the body, enabling movement and sensation.