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Interpret this geometrically

  1. Apr 16, 2009 #1
    Hi,

    I'm trying to get an idea of what this is in my head but I do not have mathematica handy.

    f:R1 to R3
    |f(t)|=1
    and f'(t)f(t)=0

    should I just imagine these as being two tangent vectors.
     
  2. jcsd
  3. Apr 16, 2009 #2
    If that is a dot product, you should already know of a common simple curve whose tangent lines are always perpendicular to the position vector of the curve. The fact that the length of the position vector is a constant should tell you that the curve is a subset of a particular common surface.
     
  4. Apr 16, 2009 #3
    Me thinks sphere.
     
  5. Apr 16, 2009 #4
    Yous thinks right.

    Well, circle I think, actually.
     
  6. Apr 17, 2009 #5
    The sphere is the right idea. Note that the curve does not need to be a circle.
     
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