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Math Help - perpendicular surface

  1. #1
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    Question perpendicular surface

    Sphere x^2 +y^2 +z^2 =a^2 can be written as
    r(phi, theta) = <asinphicostheta,asinphisintheta, acosphi>

    0< or = phi < or = pi, 0< or = theta < or = 2pi.

    Show that the radius vector r is normal to the tangent plane at each point on the sphere.

    Thank you very much.
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  2. #2
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    Quote Originally Posted by kittycat View Post
    Sphere x^2 +y^2 +z^2 =a^2 can be written as
    r(phi, theta) = <asinphicostheta,asinphisintheta, acosphi>

    0< or = phi < or = pi, 0< or = theta < or = 2pi.

    Show that the radius vector r is normal to the tangent plane at each point on the sphere.

    Thank you very much.
    Hint: Show that the gradient is orthogonal to the tangent vector.
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