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

question 7

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:

Probability of Success

The likelihood or chance of an event or endeavor achieving its intended outcome or goal.

Probability of Failure

This refers to the likelihood that a system or component will fail to perform its intended function within a specified period.

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Preemptive Nuclear Attack

A nuclear strike launched with the belief that an enemy is about to carry out a nuclear attack.