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Trouble understanding method to compute unit normal vector for a parametric curve

  1. Jun 1, 2010 #1
    The unit normal vector N of a given curve is equal to the first derivative with respect to t of the unit tangent vector T'(t)divided by the norm of T'(t) (For a parametric vector equation of parameter t.)

    I realize this works because T(t) is orthogonal to T'(t), but I don't understand why the derivative of the vector T is orthogonal to T itself.

    Can anyone explain to me why the derivative of a tangent vector is orthogonal to the tangent vector? Thanks.
  2. jcsd
  3. Jun 1, 2010 #2


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    In general it is not true but if the tangent vectors have constant length then the derivative of the length is zero.
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