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Math Help - Parametric/Symmetric equations

  1. #1
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    Parametric/Symmetric equations

    Find parametric equations and symmetric equations for the line.

    The line through (1,-1,1) and parallel to the line x + 2 = (1/2)y = z - 3.

    My solution:

    (X0, Y0, Z0) = (1,-1,1)
    v = (a,b,c) = <1,1/2,1>


    x -1 = (y +1)/(1/2) = z -1

    x = 1 + t
    y = -1 + 1/2t
    z = 1 + t

    The answer is:

    x - 1 = (y + 1) / 2 = z - 1

    x = 1 + t
    y = -1 + 2t
    z = 1 + t

    I'm confused where the 2 came from in the y equation.
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  2. #2
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    Quote Originally Posted by kenshinofkin View Post
    Find parametric equations and symmetric equations for the line.

    The line through (1,-1,1) and parallel to the line x + 2 = (1/2)y = z - 3.

    My solution:

    (X0, Y0, Z0) = (1,-1,1)
    v = (a,b,c) = <1,1/2,1>


    x -1 = (y +1)/(1/2) = z -1

    x = 1 + t
    y = -1 + 1/2t
    z = 1 + t

    The answer is:

    x - 1 = (y + 1) / 2 = z - 1

    x = 1 + t
    y = -1 + 2t
    z = 1 + t

    I'm confused where the 2 came from in the y equation.
    x + 2 = (1/2)y = z - 3:

    x + 2 = t => x = t - 2
    y/2 = t => y = 2t
    z - 3 = t => z = t + 3

    So a vector in the direction of this line is (1, 2, 1).

    So the required line will have vector equation r = (1, -1, 1) + t(1, 2, 1) and the parametric and symmetric equations follow easily.
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