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Math Help - FInding Points of Tangent Line w/ Vectors

  1. #1
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    FInding Points of Tangent Line w/ Vectors

    1. The problem statement, all variables and given/known data

    Consider the ellipsoid 4x^2+2y^2+z^2 = 19. Find all the points where the tangent plane to this ellipsoid is parallel to the plane 2y−8x+z = 0.





    3. The attempt at a solution

    So I found the normal vector to the tangent, <8x,4y,2z>.

    I also found the normal vector to the plane, <-8,2,1>

    So what step do I do next? I'm Confused on where to go after this.
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  2. #2
    MHF Contributor FernandoRevilla's Avatar
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    All right, now:

    \dfrac{8x}{-8}=\dfrac{4y}{-2}=\dfrac{2z}{1}

    Equivalently:

    x=-2z,\;y=z

    Then, substitute that in the ellipsoide equation.

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    Fernando Revilla
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  3. #3
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    Thanks,

    I got, (-2,1,1)
    and (2,-1,-1)
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  4. #4
    MHF Contributor FernandoRevilla's Avatar
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    All right.

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    Fernando Revilla
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