#### Answer

$\textbf{r} = \langle 1,0,1\rangle + t\langle2,-3,2 \rangle$

#### Work Step by Step

Equation of a Line: $\textbf{r} = \textbf{r}_0 + t\textbf{v}$
$\textbf{r}_0 = \langle 1,0,1\rangle$
Given the two points, we can find $\textbf{v}$:
$\textbf{v} = \langle3-1, -3-0, 3-1\rangle = \langle 2, -3, 2\rangle$
$\textbf{r} = \langle 1,0,1\rangle + t\langle2,-3,2 \rangle$