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

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

Correct Answer:

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