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Equation tangent with a plane

  1. Feb 19, 2009 #1
    1. The problem statement, all variables and given/known data

    Find the equation of the tangent plane at (2,3,2) to the surface below.
    x^2 + y^2 - xyz = 1

    The question asks me to do this in two way, one is to view the surface as the graph of a function of two variables z = g(x,y). and the other one is to view the surface as a level surface for a function f(x,y z).

    2. Relevant equations



    3. The attempt at a solution

    For the first part, I already got an answer of z = (-x+y+5)/3, and so the answer to the second one I assume is x-y+3z-5 = 0. but why is it wrong? am I doing something wrong here?
     
  2. jcsd
  3. Feb 19, 2009 #2

    Dick

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    z = (-x+y+5)/3 and x-y+3z-5 = 0 are the same plane. How can one be right and the other one be wrong?
     
  4. Feb 19, 2009 #3
    That's why I am confused as well... I thought I misunderstand the question for a reason... as one asks to answer it to view the surface as the graph of a func of two variables and the other one as three...
     
  5. Feb 19, 2009 #4

    Dick

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    One is probably suggesting you use a cross product and the other to use a gradient to find the normal. But they should both give you the same answer. And they do. Why do you think it's wrong?
     
  6. Feb 19, 2009 #5
    I don't think it's wrong, I think it's correct, but it's a web assign problem and when I submit the answer above it marks it as wrong. However the z = (-x+y+5)/3 is accepted
     
  7. Feb 19, 2009 #6

    Dick

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    That's web assign's problem. Who do you believe? I think you are correct.
     
  8. Feb 19, 2009 #7
    ok then... hoping for some more inputs
     
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