Answer
$2x-y+z=0$
Work Step by Step
Here, the level curve for $f(x,y,z)=\dfrac{x-y+z}{2x+y-z}$ has the form of $c=\dfrac{x-y+z}{2x+y-z}$
As we are given that $x=1,y=0,z=-2$
Then $c=\dfrac{1-0+(-2)}{2+0-(-2)}$
or, $ c=\dfrac{1-0-2}{2+0+2}=-\dfrac{1}{4} $
Now, $c=\dfrac{x-y+z}{2x+y-z} \implies -(\dfrac{1}{4}) =\dfrac{x-y+z}{2x+y-z}$
or, $6x-3y+3z=0$
Hence, $2x-y+z=0$
