Suppose the Two Particles Travel Along the Space Curves $\mathbf { r } ( t ) = t ^ { 2 } \mathbf { i } + ( 8 t - 16 ) \mathbf { j } + t ^ { 2 } \mathbf { k }$

Multiple Choice

Suppose the two particles travel along the space curves $\mathbf { r } ( t ) = t ^ { 2 } \mathbf { i } + ( 8 t - 16 ) \mathbf { j } + t ^ { 2 } \mathbf { k }$ and $\mathbf { u } ( t ) = ( 3 t + 4 ) \mathbf { i } + t ^ { 2 } \mathbf { j } + ( 5 t - 4 ) \mathbf { k }$ . A collision will occur at the point of intersection $P$ if both particles are at $P$ at the same time. Find the point of collision.

A) $( 9,9,9 )$
B) $( 9,16,9 )$
C) $( 16,9,16 )$
D) $( 16,16,16 )$
E) $( 8,8,8 )$