Given that the acceleration vector is $\mathbf{a} \left( t \right) = \left( -9 \cos \left( -3 t \right) \right) \mathbf{i} + \left( -9 \sin \left( -3 t \right) \right) \mathbf{j} + \left( 1 t \right) \mathbf{k}$, the initial velocity is $\mathbf{v} \left( 0 \right) = \mathbf{i + k}$, and the initial position vector is $\mathbf{r} \left( 0 \right) = \mathbf{i + j + k}$, 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: the coefficients in your answers must be entered in the form of expressions in the variable \emph{t}; e.g. "5 cos(2t)"