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Thread: [SOLVED] Vector Proof - Parallelogram and Triangle

  1. #1
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    [SOLVED] Vector Proof - Parallelogram and Triangle



    The quadrilateral OABC is a parallelogram, and $\displaystyle \vec{OC} = 3\vec{CD}$

    Now, let $\displaystyle \vec{AE} = m \times \vec{OA}$ and $\displaystyle \vec{BE} = n \times \vec{DB}$, where $\displaystyle m, n \in R^+$. Find the value of $\displaystyle m$ and $\displaystyle n$.


    I can't seem to find how to calculate $\displaystyle m$ and $\displaystyle n$, anyone know how to?
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  2. #2
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    Similar Triangles

    Hello Enedrox

    Welcome to Math Help Forum!
    Quote Originally Posted by Enedrox View Post


    The quadrilateral OABC is a parallelogram, and $\displaystyle \vec{OC} = 3\vec{CD}$

    Now, let $\displaystyle \vec{AE} = m \times \vec{OA}$ and $\displaystyle \vec{BE} = n \times \vec{DB}$, where $\displaystyle m, n \in R^+$. Find the value of $\displaystyle m$ and $\displaystyle n$.


    I can't seem to find how to calculate $\displaystyle m$ and $\displaystyle n$, anyone know how to?
    Note that triangles DCB, BAE and DOE are all similar, because of the parallel lines.

    So $\displaystyle \vec{DO} = 4\vec{DC} \Rightarrow \vec{DE}=4\vec{DB}$

    $\displaystyle \Rightarrow \vec{BE}=3\vec{DB}$

    $\displaystyle \Rightarrow n = 3$

    and $\displaystyle \vec{EO}=4\vec{BC}=4\vec{AO}$

    $\displaystyle \Rightarrow \vec{AE} = 3\vec{OA}$

    $\displaystyle \Rightarrow m = 3$

    Grandad
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  3. #3
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    wow, well that was easy. I was thinking WAY too hard lol

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