Example 3. Derive the equation of the plane parallel to the $O z$ axis and passing through the points $(1,0,1)$ and $(-2,1,3)$.
Solution. The equation of a plane parallel to the $O z$ axis has the form $A x+B y+D=0$. Substituting the coordinates of the given points of the plane into this, we obtain a system for determining the coefficients of the equation:

$$
\left\{\begin{array}{l}
A \cdot 1+B \cdot 0+D=0, \\
A \cdot(-2)+B \cdot 1+D=0
\end{array} \Rightarrow D=-A, B=3 A\right.
$$

i.e., $A x+3 A y-A=0$, or $x+3 y-1=0$.