Solved: ?For the following exercises, find parametric equations for the normal line to

Chapter 4, Problem 186

(choose chapter or problem)

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 \(\mathbf{n}=\langle a, b, c\rangle\) that is parallel to the line. Then the equation of the line is \(x-x_{0}=a t, y-y_{0}=b t, z-z_{0}=c t\).)

\(z=e^{4 x^{2}+6 y^{2}}, P(0,0,1)\)

Text Transcription:

P_0_left(x_0,y_0,z_0_right)

mathbf_n=langle_a,b,c_rangle

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

z=e^4x^2+6y^2,P(0,0,1)