For the Curve Given By $\mathbf { r } ( t ) = (4 \sin t , 5 t , 4 \mathrm { cos } t )$

question 55

Multiple Choice

For the curve given by $\mathbf { r } ( t ) = (4 \sin t , 5 t , 4 \mathrm { cos } t )$ , find the unit normal vector. $\mathbf { a } ( t ) = 2 \mathbf { k } , \mathbf { v } ( 0 ) = 10 \mathbf { i } - 9 \mathbf { j }$

• A) \(( 2 \sin t , 5 , - 2 \cos t)\)
• B) \((- 2 \sin t , 0 , - 2 \cos t )\)
• C) \(\left( - \frac { \sin t } { \sqrt { 29 } } , 0 , - \frac { \cos t } { \sqrt { 29 } } \right)\)
• D) \(( \sqrt { 29 } \sin t , 0 , - \sqrt { 29 } \mathrm { cost } )\)
• E) None of these

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Definitions:

Wernicke's Area

A region of the brain located in the temporal lobe that is involved in the understanding of spoken language.

Prefrontal Cortex

The front part of the frontal lobe of the brain, involved in decision making, problem-solving, control of purposeful behaviors, and emotion regulation.

Executive Control System

A term often used interchangeably with executive control centre, refering to the brain networks involved in high-level cognitive functions such as decision making.

Corpus Callosum

A large band of neural fibers connecting the two hemispheres of the brain, facilitating communication between them.