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 $\vec { r } ( t )$

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The Answer of 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 $\vec { r } ( t )$

Given the Acceleration Vector a⃗(t)=⟨2t,cos⁡(t),12t2⟩\vec { a } ( t ) = \left\langle 2 t , \cos ( t ) , 12 t ^ { 2 } \right\ranglea(t)=⟨2t,cos(t),12t2⟩

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