Answer
a) $2x+ 2y+z=4$;
b) $x=0+2t=2t,y=1+2t; z=2+t$
Work Step by Step
a. The vector equation is given as: $r(x,y,z)=r_0+t \nabla f(r_0)$
The equation of tangent line is given by $\nabla f(0,1,2)=\lt 2,2,1 \gt$
Now, $(2)(x-0)+(2)(y-1)+(1)(z-2)=0 \implies 2x+ 2y+z=4$
b. The vector equation is given as: $r=r_0+t \nabla f(r_0)$
The parametric equations are:
$x=0+2t=2t,y=1+2t; z=2t$
Thus, $x=2t,y=1+2t; z=2+t$
