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Math Help - General vector equation proof

  1. #1
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    General vector equation proof

    A curve is defined by r(t) such that r'(t) \neq 0
    T(t)=\frac{r'(t)}{|r'(t)|}

    Show that T and T' are always orthogonal by using |T|=1

    edit: this should only take a few lines of working
    i've tried using dot product =0 because the angle is 90 but i've no idea where to take that from there
    Last edited by Rubberduckzilla; November 22nd 2009 at 03:50 PM.
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  2. #2
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    Quote Originally Posted by Rubberduckzilla View Post
    A smooth curve is defined by r(t) such that r'(t) \neq 0
    The unit tangent vector is T(t)=\frac{r'(t)}{|r'(t)|}

    Show that T and T' are always orthogonal by using |T|=1

    edit: i've been told that this should only take a few lines of working
    i've tried using dot product =0 because the angle is 90 but i've no idea where to take that from there
    |T| = 1 tells you that T.T = 1. Differentiate that (product rule): T'.T + T.T' = 0. That's it (less than one line of working)!
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  3. #3
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    I accept with information:A curve is defined by r(t) such that r'(t) \neq 0
    T(t)=\frac{r'(t)}{|r'(t)|}
    Show that T and T' are always orthogonal by using |T|=1
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