Answer
a) $-2x+z=-2$ b) $x=2-4t,y=0; z=2+2t$
Work Step by Step
a) Since, we have the vector equation $r(x,y,z)=r_0+t \nabla f(r_0)$
The equation of the tangent line is: $\nabla f(2,0,2)=\lt -4,0,2 \gt$
Thus, $-4(x-2)+0(y-0)+2(z-2)=0$
or, $-4x+2z=-4 \implies -2x+z=-2$
b) Since, we have the vector equation $r=r_0+t \nabla f(r_0)$
Now, the parametric equations of $\nabla f(2,0,2)=\lt -4,0,2 \gt$ are
$x=2-4t,y=0; z=2+2t$
