Answer
a) $2y+3z=7$
b) $x=1,y=-1+4t; z=3+6t$
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: $\nabla f(1,-1,3)=\lt 0,4,6 \gt$
Thus, $0(x-1)+4(y+1)+6(z-3)=0$
or, $4y+6z=14 \implies 2y+3z=7$
b) Since, we have the vector equation $r=r_0+t \nabla f(r_0)$
Now, the parametric equations are:
$x=1+0t=1,y=-1+4t; z=3+6t$
