Answer
a) $-2x+z=-2$ and b) $x=2-4t,y=0; z=2+2t$
Work Step by Step
a. The vector equation is given by: $r(x,y,z)=r_0+t \nabla f(r_0)$
The equation of tangent line is given as: $\nabla f(2,0,2)=\lt -4,0,2 \gt$
Now, $-4(x-2)+0(y-0)+2(z-2)=0$
or, $-4x+2z=-4$
This implies that $-2x+z=-2$
b. The vector equation is given by: $r(x,y,z)=r_0+t \nabla f(r_0)$
The parametric equations for $\nabla f(2,0,2)=\lt -4,0,2 \gt$ are:
$x=2-4t,y=0; z=2+2t$
