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Math Help - How to convert cartesian equations into vector or parametric equations?

  1. #1
    Junior Member JoeyCC's Avatar
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    How to convert cartesian equations into vector or parametric equations?

    Ok I am having difficulties converting cartesian into equations to parametric/vector equations.

    By using the example provided could someone show me how it's done?
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  2. #2
    MHF Contributor
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    Let A(1,5) and u(3,2)
    M(x,y) is on the line passing through A with direction u means that exists k real such as AM = k u
    Coordinates give the system
    x - 1 = 3k
    y - 5 = 2k

    Parametric equation of the line is the system
    x = 3k + 1
    y = 2k + 5

    To get the cartesian equation you have to eliminate k
    2x = 6k + 2
    3y = 6k + 15

    Difference gives 2x - 3y = -13
    A cartesian equation is therefore 2x - 3y + 13 = 0
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  3. #3
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    Hello, JoeyCC!


    I believe the vector is: . \vec v \;=\;(1+3t)\vec i + (5 + 2t)]\vec j

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  4. #4
    Junior Member JoeyCC's Avatar
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    Thanks Man!
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