Answer
a) $2x+ 2y+z=4$
b) $x=0+2t=2t,y=1+2t; z=2+t$
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: $\nabla f(0,1,2)=\lt 2,2,1 \gt$
Thus, $2(x-0)+2(y-1)+1(z-2)=0$
or, $2x+ 2y+z=4$
b) Since, we have the vector equation $r=r_0+t \nabla f(r_0)$
Now, the parametric equations are:
$x=0+2t=2t,y=1+2t; z=2+t$
