Chapter 12 - Vectors and the Geometry of Space - 12.5 Equations of Lines and Planes - 12.5 Exercises - Page 871: 32

$3x+2y-5z=0$

The general form of the equation of the plane is: $x+ay+bz=c$ Since, the plane passes through the origin, thus, $c=0$ $x+ay+bz=0$ Plugging in the values $(3,-2,1)$, we get $3+a(-2)+b(1)=0$ $3-2a+b=0$ $2a-b=3$ ...(1) Plugging in the values $(1,1,1)$, we get $1+a(1)+b(1)=0$ $a+b=-1$...(2) Add equations (1) and (2), after simplification, we get $3x+2y-5z=0$