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Math Help - Vector equation proof

  1. #1
    Junior Member NoFace's Avatar
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    Vector equation proof

    I really have no idea how to attack this one.

    If a curve has the property that the position vector r(t) is always perpendicular to the tangent vector r'(t), show that the curve lies on a sphere with the center at the origin.

    Thanks
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  2. #2
    MHF Contributor

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    Quote Originally Posted by NoFace View Post

    If a curve has the property that the position vector r(t) is always perpendicular to the tangent vector r'(t), show that the curve lies on a sphere with the center at the origin.
    so we have r(t) \cdot r'(t)=0, which gives us: (r(t) \cdot r(t))'=2r(t) \cdot r'(t)=0. thus: ||r(t)||^2=r(t) \cdot r(t)=c, for some constant c. so the curve lies on: x^2 + y^2 + z^2 = c. \ \ \square
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