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Math Help - Parametric equations, parallel line

  1. #1
    Member nautica17's Avatar
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    Parametric equations, parallel line

    This is a question from my calculus 3 class.

    "Find the parametric equation of the line through the origin that is parallel to the line given by x = 1, y = -1 + t, z = 2."

    I'm not sure if I did this right, and frankly I'm still a little uneasy with parametric equations.

    So to begin, I made a vector out of the parametric equations they gave me just for the heck of it:
    v = <1, 1, 0>

    In the given equations:
    x_0 = 0
    y_0 = -1
    z_0 = 2

    And so the parallel line would have:
    x_0 = 0
    y_0 = 0
    z_0 = 0

    Making the parallel parametric equations through the origin:
    x = t
    y = t
    z = t

    I don't feel this is correct, but my logic behind the answer is that if the line goes through the origin, then only the above parametric equations work right? Honestly I'm confused. I guess I need a bump in the right direction.
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  2. #2
    Member nautica17's Avatar
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    Or wait.. would the equations be:
    x = t
    y = t
    z = 0
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  3. #3
    MHF Contributor FernandoRevilla's Avatar
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    \begin{Bmatrix}x=0\\y=t\\z=0\end{matrix} \quad (t\in\mathbb{R})


    Fernando Revilla
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  4. #4
    Member nautica17's Avatar
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    I'm a little confused on how to get that answer.

    I'm going by the equations:
    x = x_0 + a*t
    y = y_0 + b*t
    z = z_0 + c*t

    And so:
    a = 1
    b = 1
    c = 0

    The x_0, y_0, and z_0 are all zero.

    And I get this:
    x = t
    y = t
    z = 0
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  5. #5
    MHF Contributor FernandoRevilla's Avatar
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    Quote Originally Posted by nautica17 View Post
    And so:
    a = 1
    b = 1
    c = 0

    According to the OP it should be:

    a=0,\;b=1,\;c=0


    Fernando Revilla
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