Answer
$x+y-z=-7$
Work Step by Step
The general form of the equation of the plane is:
$a(x-x_0)+b(y-y_0)+c(z-z_0)=0$
or, $ax+by+cz=ax_0+by_0+cz_0$
The required equation of the required plane is of the form: $z=x+y+k$
Put $x=3,y=-2, z=8$ and solve for $k$.
After simplification, we get
$8=3-2+k$
$k=7$
Hence, $x+y-z=-7$
