Find the Unit Tangent Vector of the Given Curve $\mathbf { T } = ( 7 \cos t ) \mathbf { j } - ( 7 \sin t ) \mathbf { k }$

question 75

Multiple Choice

Find the unit tangent vector of the given curve.
-r(t) = (7t cos t - 7 sin t) j + (7t sin t + 7 cos t) k

• A) \(\mathbf { T } = ( 7 \cos t ) \mathbf { j } - ( 7 \sin t ) \mathbf { k }\)
• B) \(\mathbf { T } = ( - 7 \sin t ) \mathbf { j } + ( 7 \cos t ) \mathbf { k }\)
• C) \(\mathbf { T } = ( - \sin t ) \mathbf { j } + ( \cos t ) \mathbf { k }\)
• D) \(\mathbf { T } = - \frac { 1 } { 7 } ( \sin t ) \mathbf { j } + \frac { 1 } { 7 } ( \cos t ) \mathbf { k }\)

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Definitions:

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A personality trait characterized by resilience, commitment, control, and acceptance of challenges.

Aggression

Behaviors or attitudes that may be directed towards others or oneself, embodying actions of anger, hostility, or violence.

Commitment

A state or quality of being dedicated to a cause, activity, or relationship, often implying a sense of obligation or responsibility.

Control

The ability to shape or control the actions of others and the direction of events.