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Homework Help: Find a vector normal to the plane at (2,1,7)

  1. Feb 26, 2012 #1
    1. The problem statement, all variables and given/known data
    This is a two part problem
    A) Find a vector normal to the plane at (2,1,7)
    B) Find a vector normal to the plane tangent to the paraboloid at (2,1,7)


    2. Relevant equations

    Plane: z = x + y +4
    Paraboloid: z = x^2 +3y^2

    3. The attempt at a solution
    I'm not sure where to start. I know that a vector normal to the plane is <1,1,-1>, but that isn't at (2,1,7). Any help?
     
  2. jcsd
  3. Feb 26, 2012 #2

    Dick

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    A plane has the same normal everywhere, doesn't it?
     
  4. Feb 26, 2012 #3
    That's what I thought at first. But it seems too easy to be the solution to both questions. I'm going to read over the section again and see if I can find anything that will be useful.
     
  5. Feb 26, 2012 #4

    Dick

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    It's not the solution to the second question. Think about using the gradient.
     
  6. Feb 26, 2012 #5
    I was able to solve it, thank you. :)
     
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