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Thread: Finding unit tangent vectors

  1. #1
    Full Member
    Join Date
    Mar 2007
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    Mount Desert Island, Maine
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    727

    Finding unit tangent vectors

    The web homework is not accepting my answer for this, even though I've done it like the others. Have I made a mistake?

    given r(t) = (t^2, t^3), find the unit tangent vector at T(t) at t = 1:

    r(t) = t^2i + t^3j

    T(t) = (t^2i + t^3j) / sqrt ( t^4 + t^6)
    T(1) = ( i + j) / sqrt(2)

    Thus: T(1) = <sqrt(2)/2 , sqrt(2)/2>

    Yes, no?

  2. #2
    Senior Member
    Join Date
    Jul 2005
    Location
    Christchurch, New Zealand
    Posts
    1,136

    Re: Finding unit tangent vectors

    If r(t) is the position vector, then the unit tangent vector is [tex]\frac{r&#39;(t)}{||r&#39;(t)||}[/tex].

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