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Thread: vector equation

  1. #1
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    vector equation

    Hello,

    Find the vector equation for the lines joining (3,7) , (5,4)

    Thanks in advance.
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  2. #2
    MHF Contributor Amer's Avatar
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    Quote Originally Posted by Oasis1993 View Post
    Hello,

    Find the vector equation for the lines joining (3,7) , (5,4)

    Thanks in advance.

    $\displaystyle slope = \frac{7-4}{3-5} = \frac{3}{-2} $

    vector equation

    $\displaystyle \frac{y-4}{x-5} = \frac{-3}{2} $

    $\displaystyle 2(y-4) = -3(x-5) $

    $\displaystyle 2y-8 = -3x+15 $

    $\displaystyle y = \frac{-3x +15 +8 }{2} $
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  3. #3
    Senior Member
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    Quote Originally Posted by Oasis1993 View Post
    Hello,

    Find the vector equation for the lines joining (3,7) , (5,4)

    Thanks in advance.
    the direction vector is $\displaystyle (5,4) - (3,7) = (2,-3)$

    the parametric equation in vector form for this line is $\displaystyle \left(
    \begin{array}
    [c]{c}%
    x\\
    y
    \end{array}
    \right) = \left(
    \begin{array}
    [c]{c}%
    3\\
    7
    \end{array}
    \right) + \left(
    \begin{array}
    [c]{c}%
    2\\
    -3
    \end{array}
    \right)t$, $\displaystyle t \in \mathbb{R}$
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