Example 2. Form the equation of the plane that intercepts segment $O A=3$ on the $O x$ axis and is perpendicular to the vector $\vec{N}=\{2,-3,1\}$.
Solution. According to the condition, the point $A(3,0,0)$ belongs to the desired plane. According to point $3^{\circ}$, the equation of this plane has the form

$$
2(x-3)-3(y-0)+(z-0)=0, \quad \text { or } \quad 2 x-3 y+z-6=0
$$