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

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