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Perpendicular line to the Surface

  1. May 13, 2012 #1
    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]0=x^2+y^2-z[/itex]
    [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?
     
  2. jcsd
  3. May 13, 2012 #2

    LCKurtz

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    When ##x=-1## and ##y=2##, ##z## isn't zero.
     
  4. May 13, 2012 #3
    Wow haha that was a horrible miscalculation on my part. Thanks for pointing that out! :redface:
     
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