#### Answer

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

#### Work Step by Step

Equation of a Line: $\textbf{r} = \textbf{r}_0 + t\textbf{v}$
Given points $(1,0,1)$ and $(0,-2,1)$
Use one of the points as $\textbf{r}_0$
$\textbf{r}_0 = \langle 1,0,1\rangle$
Given the two points, we can find $\textbf{v}$:
$\textbf{v} = \langle0-1, -2-0, 1-1\rangle = \langle -1,-2,0\rangle$
$\textbf{r} = \langle 1,0,1\rangle + t\langle-1,-2,0 \rangle$