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Parameterized tangent line to a parameterized curve

  1. Feb 10, 2009 #1
    1. The problem statement, all variables and given/known data

    I seem to remember that a parameterized a(t) curve in [tex]\mathbb{R}^3[/tex] that one can construct the tangent from the slope of a'(t) and the curve itself.

    such that the tangent line L = a(t) + s * a'(t) to a. This is supposedly a straight line in [tex]\mathbb{R}^3[/tex].
    To make a long question. What theorem allows me to construct the tangent in such a way? confused:
  2. jcsd
  3. Feb 10, 2009 #2


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    Hi Cauchy1789! :smile:

    It's the theorem that says that the slope of the tangent euqals the derivative …

    so, for fixed t, L(s) = s * a'(t) + constant …

    and the constant has to be a(t) because L(0) = a(t). :wink:
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