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