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Math Help - Tangential component help

  1. #1
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    Tangential component help

    1.)
    r(t) = < t, t^2, 1/t >
    r'(t) = < 1, 2t, -1/t^2>
    r"(t) = < 0, 2, 1/t^4>
    |r'(t)| = squartroot (1 + 4t^2 + 1/t^4)


    (a) Find the tangential component of the particle’s acceleration vector at time t = 1.

    r'(1) = < 1, 2, -1>
    r"(1) = < 0, 2, 1>
    |r'(1)|= squareroot ( 1 + 4 +1)

    Tangential component = r'(1) dot r"(1) / |r'(1)| = 0 + 4 -1 = 3/ sqroot 6




    (b) Find all values of t at which the particle’s velocity vector is orthogonal to the particle’s acceleration vector.


    Is part a right?
    How do I find part b?


    2.)
    <4t, 5t^3, 2t^2>
    a.) Find the unit tangent vector T(t) at the point where t = 1.

    r'(1) = <4, 15, 4>
    r"(1) = <0, 30, 4>
    T(1) = 32/(sqrt(916))

    b.) Find the parametric equations of the tangent line the curve at the point where t = 1




    Thanks in advanced
    Last edited by khuezy; November 16th 2008 at 09:43 AM.
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  2. #2
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    ?

    can anyone help please?
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  3. #3
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    hi

    can anyone help me with this problem?
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