Chapter 12: Vectors and the Geometry of Space - Section 12.5 - Lines and Planes in Space - Exercises 12.5 - Page 727: 30

$x+y-2z=7$

The standard equation of plane passing through the point $(a,b,c)$ is given as $p(x-a)+q(y-b)+r(z-c)=0$ The equation of normal to the plane; $n=\lt -2,-2,4 \gt$ For point $(0,3,-2)$, we get $(-2)(x-0)+(-2)(y -3)+(4)(z+2)=0$ or, $-2x-2y+4z=-14$ Thus, $x+y-2z=7$