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Math Help - Intersection between two lines

  1. #1
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    Intersection between two lines

    Hi there. I got this exercise, where I must find the intersection between these two lines:


    L_1=2x-y=2

    L_2=\begin{Bmatrix} x=-1+2\lambda & \mbox{ }& \\y=-1 & \mbox{}& \end{matrix}

    I've parametrized L_1

    P_0(1,0)\in{L_1} y P_1(0,-2)\in{L_1}

    From these points of L_1 I found a vector parallel to L_1: u=(-1,-2)

    And then: L_1=\begin{Bmatrix} x=1-\lambda & \mbox{ }& \\y=-2\lambda & \mbox{}& \end{matrix}

    L_1\cap{L_2}=\begin{Bmatrix} -1+2\lambda=1-\lambda & \mbox{ }& \\-1=-2\lambda & \mbox{}& \end{matrix}\Longrightarrow{\begin{Bmatrix} \lambda=\displaystyle\frac{3}{2} & \mbox{ }& \\\displaystyle\frac{1}{2}=\lambda & \mbox{}& \end{matrix}}

    Lambda should be in both equations \displaystyle\frac{1}{2}, but for x it gives me \displaystyle\frac{3}{2}, and I don't know where the error is.

    Any help would be appreciated.

    Well, I don't know where is the error on my latex code neither
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  2. #2
    Member
    Joined
    Nov 2009
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    Quote Originally Posted by Ulysses View Post
    Hi there. I got this exercise, where I must find the intersection between these two lines:


    L_1=2x-y=2

    L_2=\begin{Bmatrix} x=-1+2\lambda & \mbox{ }& \\y=-1 & \mbox{}& \end{matrix}

    I've parametrized L_1

    P_0(1,0)\in{L_1} y P_1(0,-2)\in{L_1}

    From these points of L_1 I found a vector parallel to L_1: u=(-1,-2)

    And then: L_1=\begin{Bmatrix} x=1-\lambda & \mbox{ }& \\y=-2\lambda & \mbox{}& \end{matrix}

    L_1\cap{L_2}=\begin{Bmatrix} -1+2\lambda=1-\lambda & \mbox{ }& \\-1=-2\lambda & \mbox{}& \end{matrix}\Longrightarrow{\begin{Bmatrix} \lambda=\displaystyle\frac{3}{2} & \mbox{ }& \\\displaystyle\frac{1}{2}=\lambda & \mbox{}& \end{matrix}}

    Lambda should be in both equations \displaystyle\frac{1}{2}, but for x it gives me \displaystyle\frac{3}{2}, and I don't know where the error is.

    Any help would be appreciated.

    Well, I don't know where is the error on my latex code neither
    Ok, I will help you.

    L1: 2x1-y1=2 or y1=2x1-2

    L2: x=-1+2t
    y=-1

    To find the intersection point you need to do this: y1=y or 2x1-2=-1 and x1=1/2, so the intersection point is (1/2,-1).

    Regards.
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