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Math Help - find a tangent plane on a sphere

  1. #1
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    find a tangent plane on a sphere

    a sphere has equation: x^2+y^2+z^2=2
    find the equation of the tangent plane at (0,1,1) on the sphere
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  2. #2
    Super Member flyingsquirrel's Avatar
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    Hi

    The tangent plane at a point M of a sphere is perpendicular to \vec{CM} where C is the centre of the sphere. This gives you a vector which is normal to the plane. As we also have that M is a point of the plane, you can determine the equation you're looking for...
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  3. #3
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    Quote Originally Posted by szpengchao View Post
    a sphere has equation: x^2+y^2+z^2=2
    find the equation of the tangent plane at (0,1,1) on the sphere
    If

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

    then the normal vector of the tangent plane can be calculated by:

    \frac{\partial f}{\partial x}i +\frac{\partial f}{\partial y}j +\frac{\partial f}{\partial z}k = 0

    With your question you get:

    2xi+2yj+2zk=0

    Plug in the coordinates of the tangent point and the normal vector is:

    \vec n = 2j+2k

    Since the point T(0, 1, 1) is located on the plane the equation of the plane becomes:

    2y+2z-4=0
    Attached Thumbnails Attached Thumbnails find a tangent plane on a sphere-tang_ankugel.gif  
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