Given that the acceleration vector is $\mathbf{a} \left( t \right) = \left( -9 \cos(-3t), -9 \sin(-3t), t \right)$,
the initial velocity is $\mathbf{v}(0) = (1,0,1)$,
and the initial position vector is $\mathbf{r}(0) = (1,1,1)$, compute:

A. The velocity vector $\mathbf{v} \left( t \right) =$ $\mathbf{i} +$ $\mathbf{j} +$ $\mathbf{k}$

B. The position vector $\mathbf{r} \left( t \right) =$ $\mathbf{i} +$ $\mathbf{j} +$ $\mathbf{k}$

Note: Your answers must be functions of $\mathbf{t}$; e.g., "5 cos(2t)"