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Math Help - [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 \vec{OC} = 3\vec{CD}

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


    I can't seem to find how to calculate m and 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 \vec{OC} = 3\vec{CD}

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


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

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

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

    \Rightarrow n = 3

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

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

    \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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