Chapter 4.4, Problem 187E

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

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

187. $z=x^2-2xy+y^2\text{at}\text{point }P(1,2,1)$