The Helix $\mathbf { r } _ { 1 } ( t ) = 4 \cos t \mathbf { i } + \sin t \mathbf { j } + t \mathbf { k }$

question 50

Multiple Choice

The helix $\mathbf { r } _ { 1 } ( t ) = 4 \cos t \mathbf { i } + \sin t \mathbf { j } + t \mathbf { k }$ intersects the curve $\mathbf { r } _ { 2 } ( t ) = ( 4 + t ) \mathbf { i } + 6 t ^ { 2 } \mathbf { j } + 5 t ^ { 3 } \mathbf { k }$ at the point $( 4,0,0 )$ . Find the angle of intersection.

• A) 0
• B) \(\frac { \pi } { 4 }\)
• C) \(\frac { \pi } { 2 }\)
• D) \(\frac { \pi } { 3 }\)
• E) None of these

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Definitions:

Fitness

The condition of being physically fit and healthy, often as a result of regular physical activity and proper nutrition.

Baseball

A bat-and-ball game played between two teams who take turns batting and fielding.

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A team sport where two teams compete to score goals by advancing a ball into the opposing team's end zone, known widely in the United States as American football and as football (soccer) elsewhere.

Physical Activity

Any bodily movement produced by skeletal muscles that requires energy expenditure, including activities undertaken while working, playing, traveling, and engaging in recreational pursuits.