Chapter 4.4, Problem 186E

For the following exercises, find parametric equations for the normal line to the surface at the indicated point. (Recall that to find the equation of a line in space, you need a point on the line, $P{0}_{}\left(x_0,y_0,z_0\right)$and a vector

n = ( a. b. c ) that is parallel to the line. Then the

equation of the line is

$x-x_0=at,y-y_0=bt,z-z_0=ct.)$

186. $z=e^{4x^2+6y^2},P\left(0,0,1\right)$