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Please tell me the definition of this problem!

  1. Nov 9, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the unique vector which is perpendicular on x2+y2=100 at (x0,y0)=(6,8).

    2. Relevant equations

    [tex]\nabla[/tex]F[tex]/[/tex] [tex]\left|[/tex] [tex]\nabla[/tex]F [tex]\left|[/tex]

    3. The attempt at a solution

    I think the solution is [tex]\nabla[/tex]F[tex]/[/tex] [tex]\left|[/tex] [tex]\nabla[/tex]F [tex]\left|[/tex] but I don't know how to calculate [tex]\nabla[/tex]F for x2+y2=100
    I know [tex]\nabla[/tex]F=([tex]\partial[/tex]F[tex]/[/tex][tex]\partial[/tex]x,[tex]\partial[/tex]F[tex]/[/tex][tex]\partial[/tex]y,[tex]\partial[/tex]F[tex]/[/tex][tex]\partial[/tex]z)
    Please tell me how I can find the answer. What is F here?
     
    Last edited: Nov 9, 2009
  2. jcsd
  3. Nov 9, 2009 #2

    Dick

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    Homework Helper

    F(x,y)=x^2+y^2-100. The level surface is F(x,y)=0. Now do the gradient. Or F(x,y)=x^2+y^2 and the level surface is F(x,y)=100, your choice.
     
  4. Nov 10, 2009 #3
    So in this case the solution is [tex]\nabla[/tex]F[tex]/[/tex][tex]\left|[/tex][tex]\nabla[/tex]F[tex]\left|[/tex] = (0.6,0.8) Is it correct?
    ([tex]\nabla[/tex]F=(2x,2y)).
     
  5. Nov 10, 2009 #4

    Dick

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    If you mean to find the unit normal to the circle, sure, that's right.
     
  6. Nov 10, 2009 #5
    Thank you very much really. I actually translated the problem from persian to English, but I think it is now correct. Again thank you very much for your great generosity.
     
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