Calculate $\mathbf{r}'(t)$ and $\mathbf{T}(t)$, where $$\mathbf{r}(t)=\langle 5+2t, 9-3t, 1+2t\rangle.$$

$\mathbf{r}'(t) = \langle$ $,$ $,$ $\rangle$.
$\mathbf{T}(t) = \langle$ $,$ $,$ $\rangle$.