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Math Help - Calculus III unit tangent and unit normal vectors

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    Calculus III unit tangent and unit normal vectors

    Consider the following vector function: r(t) = {2t*sqrt(2),e^2t,e^-2t}.

    (a) Find the unit tangent and unit normal vectors T(t) and N(t).

    (b) Finding the curvature (k(t).


    Thanks!
    Last edited by jessie546311; February 15th 2013 at 12:52 PM.
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    Re: Calculus III unit tangent and unit normal vectors

    Quote Originally Posted by jessie546311 View Post
    Consider the following vector function: r(t) = {2t*sqrt(2),e^2t,e^-2t}.
    (a) Find the unit tangent and unit normal vectors T(t) and N(t).

    (b) Finding the curvature (k(t).

    T=\frac{R'}{\|R'\|}, N=\frac{T'}{\|T'\|}=\frac{R\times(R''\times R')}{\|R\times(R''\times R')\|}

    \kappa(t)=\frac{R'\times R''}{\|R'\|^3}
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