# Perpendicular line to the Surface

by τheory
Tags: line, perpendicular, surface
 P: 43 1. The problem statement, all variables and given/known data Consider the line perpendicular to the surface $z=x^2+y^2$ at the point where x = −1 and y = 2 Find a vector parametric equation for this line in terms of the parameter t. 3. The attempt at a solution I wasn't quite sure how to go about with this problem so I just went along with the following ideas. I first took the gradient of the function at that point: $0=x^2+y^2-z$ $∇F(x,y,z)= <2x,2y,-1>$ $∇F(-1,2,0)= <-2,4,-1>$ Then I constructed the vector parametric equation of the line at that point: $L(t) = P + t∇F$ $L(t) = <-1,2,0> + t<-2,4,-1>$ Afterwards, I submitted this equation, only finding that it was incorrect; can someone explain to me what went wrong here?
 PF Patron HW Helper Thanks P: 6,756 When ##x=-1## and ##y=2##, ##z## isn't zero.
 P: 43 Wow haha that was a horrible miscalculation on my part. Thanks for pointing that out!

 Related Discussions Calculus & Beyond Homework 2 Calculus & Beyond Homework 0 Differential Geometry 1 Calculus & Beyond Homework 6 Calculus & Beyond Homework 11