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Multivar calc

  1. Apr 19, 2007 #1
    1. The problem statement, all variables and given/known data


    5. Find parametric equations for the tangent line to the curve of intersection of the surfaces
    z^2 = x^2 + y^2 and x^2 + 2y^2 + z^2 = 66 at the point (3, 4, 5).


    3. The attempt at a solution

    f(x,y,z) = x^2 + y^2 - z^2
    g(x,y,z) = x^2 + 2y^2 + z^2

    Partial derivz:

    f'x = 2x
    f'y = 2y
    f'z = -2z

    g'x = 2x
    g'y = 4y
    g'z = 2z

    grad f = <2x,2y,-2z>
    grad g = <2x,4y,2z>


    grad f (3,4,5) = < 6,8,-10>
    grad g (3,4,5) = <6,16,10>

    then v = [(grad f) X (grad g )(cross product)

    = |i j k | = 180i + 220j - 48k
    |6 8 -10|
    |6 16 10|


    this approach is wrong because the solutions manual gives me

    -10i + 4j - 2k for that vector


    please help.

    Thanks
     
  2. jcsd
  3. Apr 19, 2007 #2

    Dick

    User Avatar
    Science Advisor
    Homework Helper

    There is something going wrong with your determinant evaluation. I get 240i-120j+48k. Also remember there is not a single tangent vector - you can always multiply by a constant and still have a tangent vector.
     
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