373. Find the equation of the plane: 1) passing through the axis $O x$ and the point $(1 ; 2 ;-3) ; 2$ ) parallel to the axis $O z$ and passing through the points $(1 ; 0 ; 1)$ and $(-2 ; 1 ; 3)$.
Solution. 1) Each plane passing through the axis $O x$ is defined by an equation of the form

$$
B y+C z=0
$$

We require that the plane passes through the point $(1 ; 2 ;-3):$

$$
2 B-3 C=0 \text { or } B=\frac{3 C}{2} .
$$

Therefore, the equation of the desired plane will be of the form

$$
\frac{3 C}{2} y+C z=0
$$

or

$$
\frac{3}{2} y+z=0
$$

or

$$
3 y+2 z=0
$$

2) Each plane parallel to the axis $O z$ is defined by an equation of the form

$$
A x+B y+D=0
$$

Since the desired plane passes through the points $(1 ; 0 ; 1)$ and ( $-2 ; 1 ; 3$ ), then $\quad\left\{\begin{array}{l}A+B \cdot 0+D=0, \\ -2 A+B+D=0 .\end{array}\right.$

From this, $D=-A, B=3 A$, therefore, the equation of the desired plane

$$
A x+3 A y-A=0
$$

or

$$
x+3 y-1=0
$$