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Math Help - vector problem

  1. #1
    Member smmmc's Avatar
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    vector problem

    Hey

    OABCDEFG is a cuboid

    -> -> ->
    OA= 3j OC=2k OD=i

    M is such that ->
    OM= 1/3 ->
    OE

    N is the midpoint of BF. Find
    a) ->
    MN



    not sure how to start, i drew a cuboid but dont know how to find the 1/3 of OE


    thanks
    Thanks
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  2. #2
    MHF Contributor
    Grandad's Avatar
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    Hello smmmc
    Quote Originally Posted by smmmc View Post
    Hey

    OABCDEFG is a cuboid

    -> -> ->
    OA= 3j OC=2k OD=i

    M is such that ->
    OM= 1/3 ->
    OE

    N is the midpoint of BF. Find
    a) ->
    MN



    not sure how to start, i drew a cuboid but dont know how to find the 1/3 of OE


    thanks
    Thanks
    I'm assuming that the vertices are labelled as in the attached diagram, so that, for instance, BF is parallel to CG, OD and AE.

    If this is the case, then \vec{BF}=\vec{OD} = \vec{i} and \vec{CB}=\vec{OA}=3\vec{j}

    \Rightarrow \vec{BN}=\tfrac12\vec{BF}=\tfrac12\vec{i}

    \Rightarrow \vec{ON} = \vec{OC}+\vec{CB}+\vec{BN}

    = 2\vec{k}+3\vec{j}+\tfrac12\vec{i}

    Also \vec{OE} = \vec{OD}+\vec{DE} = \vec{i}+3\vec{j}

    \Rightarrow \vec{OM} = \tfrac13\vec{OE}=\tfrac13\vec{i} + \vec{j}

    Now \vec{ON}=\vec{OM}+\vec{MN}

    \Rightarrow \vec{MN} = \vec{ON}-\vec{OM}

    = 2\vec{k}+3\vec{j}+\tfrac12\vec{i}-\tfrac13\vec{i} - \vec{j}

    =\tfrac16\vec{i}+2\vec{j}+2\vec{k}

    Grandad
    Attached Thumbnails Attached Thumbnails vector problem-untitled.jpg  
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