Answer
a) $9x-7y-z=21$
b) $x=2+9t,y=-3-7t; z=18-t$
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: $\nabla f(2,-3,18)=\lt 9,-7,-1 \gt$
Thus, $9(x-2)-7(y+3)-1(z-18)=0$
or, $9x-7y-z=21$
b) Since, we have the vector equation $r=r_0+t \nabla f(r_0)$
Now, the parametric equations are:
$x=2+9t,y=-3-7t; z=18-t$
