Given the Acceleration Vector $\vec { a } ( t ) = \left\langle 2 t , \cos ( t ) , 12 t ^ { 2 } \right\rangle$

Essay

Given the acceleration vector $\vec { a } ( t ) = \left\langle 2 t , \cos ( t ) , 12 t ^ { 2 } \right\rangle$ and initial velocity and position $\vec { v } ( 0 ) = \langle 1,2,1 \rangle$ and $\vec { r } ( 0 ) = \langle 1,1,1 \rangle$ , find $\vec { r } ( t )$