Find a vector equation for the line through the point P = (-3, 1, -3) and parallel to the vector $\mathbf{v}$ = (3, 5, -3).
Assume $\mathbf{r}(0) = -3\!\mathbf{i} + 1\!\mathbf{j} - 3\!\mathbf{k}$ and that $\mathbf{v}$ is the velocity vector of the line.
$\mathbf{r}$(t) = $\mathbf{i}$ + $\mathbf{j}$ + $\mathbf{k}$