Perpendicular line to the Surface

by τheory
Tags: line, perpendicular, surface
τheory is offline
May13-12, 07:21 PM
P: 43
1. The problem statement, all variables and given/known data
Consider the line perpendicular to the surface [itex]z=x^2+y^2[/itex] 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:

[itex]∇F(x,y,z)= <2x,2y,-1>[/itex]
[itex]∇F(-1,2,0)= <-2,4,-1>[/itex]

Then I constructed the vector parametric equation of the line at that point:

[itex]L(t) = P + t∇F[/itex]
[itex]L(t) = <-1,2,0> + t<-2,4,-1>[/itex]

Afterwards, I submitted this equation, only finding that it was incorrect; can someone explain to me what went wrong here?
Phys.Org News Partner Science news on
Going nuts? Turkey looks to pistachios to heat new eco-city
Space-tested fluid flow concept advances infectious disease diagnoses
SpaceX launches supplies to space station (Update)
LCKurtz is offline
May13-12, 07:26 PM
HW Helper
PF Gold
LCKurtz's Avatar
P: 7,198
When ##x=-1## and ##y=2##, ##z## isn't zero.
τheory is offline
May13-12, 07:28 PM
P: 43
Wow haha that was a horrible miscalculation on my part. Thanks for pointing that out!

Register to reply

Related Discussions
Find equation of the line which is perpendicular to the line Calculus & Beyond Homework 2
LinAlg: Parametric Equation of a Line, given a parallel plane and perpendicular line Calculus & Beyond Homework 0
Calculate point on line, perpendicular and intersecting another line in 3d space Differential Geometry 1
Find equation of line that is perpendicular to the tangent line to the curve Calculus & Beyond Homework 6
Vector equation for a line passing through a point and perpendicular to another line Calculus & Beyond Homework 11