The Solution $\mathbf { r } ( t )$ To the Differential Equation

Multiple Choice

The solution $\mathbf { r } ( t )$ to the differential equation $\mathbf { r } ^ { \prime } ( t ) = 3 \cos t \mathbf { i } - 2 \sin t \mathbf { j } + \mathbf { k }$ with the condition $\mathbf { r } ( 0 ) = 2 \mathbf { i } + \mathbf { k }$ is

A) $( 3 \sin t + 2 ) \mathbf { i } - ( 2 \cos t - 2 ) \mathbf { j } + ( t + 1 ) \mathbf { k }$
B) $( 3 \sin t + 2 ) \mathbf { i } + ( 2 \cos t - 2 ) \mathbf { j } + ( t + 1 ) \mathbf { k }$
C) $( 3 \sin t + 2 ) \mathbf { i } + ( 2 \cos t - 2 ) \mathbf { j } - ( t + 1 ) \mathbf { k }$
D) $( 3 \sin t + 2 ) \mathbf { i } + ( 2 \cos t - 2 ) \mathbf { j } + ( t - 1 ) \mathbf { k }$
E) $( 3 \sin t + 2 ) \mathbf { i } - ( 2 \cos t - 2 ) \mathbf { j } + ( t - 1 ) \mathbf { k }$