Find a vector parametric equation $\vec{r}(t)$ for the line through the points $P = \left(-3,1,-3\right)$ and $Q = \left(0,6,-3\right)$ for each of the given conditions on the parameter $t$.

(a) If $\vec{r}(0) = \left<-3,1,-3\right>$ and $\vec{r}(3) = \left<0,6,-3\right>$, then
$\vec{r}(t) =$

(b) If $\vec{r}(6) = P$ and $\vec{r}(9) = Q$, then
$\vec{r}(t) =$

(c) If the points $P$ and $Q$ correspond to the parameter values $t = 0$ and $t = -3$, respectively, then
$\vec{r}(t) =$