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Homework Help: Vector function, position and tangent vectors

  1. Sep 30, 2008 #1
    1. The problem statement, all variables and given/known data
    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 center at the origin


    2. Relevant equations

    3. The attempt at a solution

    I have no idea how to even approach this problem, if somebody could give me a nudge in the right direction it would be much appreciated.
     
  2. jcsd
  3. Sep 30, 2008 #2

    Dick

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    Differentiate r(t).r(t) (the dot product).
     
  4. Sep 30, 2008 #3
    Ah, I get it now.

    We know that r(t).r(t)=|r(t)|^2. Differentiating the dot product we get:

    d/dt [r(t).r(t)]= 2r'(t).r(t) = 0 (as r'(t) is orthogonal to r(t))

    thus |r(t)|^2 is constant, and so |r(t)| is constant, which corresponds to a sphere with the centre at the origin.

    Thanks Dick :)
     
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