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Tangential Planes Problem?

  1. Dec 18, 2013 #1
    1. The problem statement, all variables and given/known data

    Find the points on the surface \(4 x^2 + 2 y^2 + 4 z^2 = 1\) at which the tangent plane is parallel to the plane \(4 x - 3 y - 2 z = 0\).

    2. Relevant equations

    Not sure

    3. The attempt at a solution

    What I did was take the gradient of both functions, the surface function as f, and the plane as g, so I got ∇f = <8x,4y,8z> and ∇g = <4,-3,-2>. Knowing that these gradients are normal vectors, and the planes would be in parallel, therefore having the same normal vectors, I set the components equal to each other and got x = 1/2, y = -3/4, z = -1/4. However, these are not the points, and I have rune out of ideas on how to work the problem.
     
  2. jcsd
  3. Dec 18, 2013 #2

    ehild

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    The normal vectors should be parallel, not equal. <8x,4y,8z>= K<4,-3,-2>, K is a constant.


    ehild
     
  4. Dec 18, 2013 #3
    Alright, I got it. Thank you very much!
     
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