Find a vector parametric equation $\vec{r}(t)$ for the line through the points $P = \left(-3,1\right)$ and $Q = \left(-6,4\right)$.

$\vec{r}(t) =$

Find a vector parametric equation $\vec{r}(t)$ for the line through the points $P = \left(5,0,-3\right)$ and $Q = \left(7,-1,-2\right)$.

$\vec{r}(t) =$

Find a vector parametric equation $\vec{r}(t)$ for the line through the points $P = \left(-1,2,3\right)$ and $Q = \left(0,-1,3\right)$.

$\vec{r}(t) =$