Answer
a) $3x+5y+4z=18$
b) $x=3+6t,y=5+10t; z=-4+8t$
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: $\nabla f(3,5,-4)=\lt 6,10,8 \gt$
Thus, $6(x-3)+10(y-5)+8(z+4)=0$
or, $6x+10y+8z=6 \implies 3x+5y+4z=18$
b) Since, we have the vector equation $r=r_0+t \nabla f(r_0)$
Now, the parametric equations are: $\nabla f(3,5,-4)=\lt 6,10,8 \gt$
$x=3+6t,y=5+10t; z=-4+8t$
