Answer
$9x-7y-z=21$
b) $x=2+9t,y=-3-7t; z=18-t$
Work Step by Step
The vector equation is given by: $r(x,y,z)=r_0+t \nabla f(r_0)$
The equation of tangent line is given as: $\nabla f(2,-3,18)=\lt 9,-7,-1 \gt$
Now, $(9)(x-2)-(7)(y+3)-(1)(z-18)=0 \implies 9x-7y-z=21$
b. The vector equation is give as: $r=r_0+t \nabla f(r_0)$
we have the parametric equations as follows:
$x=2+9t,y=-3-7t; z=18-t$
