Answer
$2x-y+z=0$
Work Step by Step
Remember that the level curve for $f(x,y,z)=\dfrac{x-y+z}{2x+y-z}$ has the form of $c=\dfrac{x-y+z}{2x+y-z}$ ...(1)
Here, we have $x=1,y=0,z=-2$
Then $c=\dfrac{1-0+(-2)}{2+0-(-2)} \implies c=-\dfrac{1}{4} $
Thus, equation (1), becomes: $-\dfrac{1}{4} =\dfrac{x-y+z}{2x+y-z} \implies 6x-3y+3z=0$
Hence, $2x-y+z=0$
