Answer
$2y-z=2$
Work Step by Step
The vector equation can be calculated as:$\nabla f(r_0) \cdot (r-r_0)=0$
The equation of the tangent for $\nabla f( 0,1,0)=\lt 0,2,-1 \gt$ is:
$0+2(y-1)-1(z-0)=0$
or, $2y-2-z=0 \implies 2y-z=2$
Hence, $2y-z=2$
