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Math Help - Vector Midpoint Problem

  1. #1
    Del
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    Vector Midpoint Problem



    What is the vector whose tail and head are the midpoint of and the midpoint of , respectively.

    Please help!
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  2. #2
    MHF Contributor red_dog's Avatar
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    The midpoint of AB is \displaystyle M\left(\frac{x_A+x_B}{2},\frac{y_A+y_B}{2},\frac{z  _A+z_B}{2}\right)
    So \displaystyle M\left(0,7,\frac{5}{2}\right)
    The midpoint of BC is \displaystyle N\left(\frac{15}{2},\frac{15}{2},\frac{9}{2}\right  )
    Then the vector is
    \displaystyle \overrightarrow{MN}=\left(x_N-x_M\right)\overrightarrow{i}+\left(y_N-y_M\right)\overrightarrow{j}+\left(z_N-z_M\right)\overrightarrow{k}=\frac{15}{2}\overrigh  tarrow{i}+\frac{1}{2}\overrightarrow{j}+2\overrigh  tarrow{k}
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  3. #3
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    Quote Originally Posted by Del View Post


    What is the vector whose tail and head are the midpoint of and the midpoint of , respectively.

    Please help!
    1. Use the midpoint formula to calculate the coordinates of head and teil of the vector \vec v

    M_{AB}\left(\frac{-5+5}2\ ,\ \frac{6+8}2\ ,\ \frac{4+1}2 \right)~\implies~ M_{AB}\left(0\ ,\ 7\ ,\ \frac{5}2 \right)

    M_{BC}\left(\frac{15}2\ ,\ \frac{15}2\ ,\ \frac{9}2 \right)

    \vec v=\overrightarrow{M_{AB} M_{BC}} = \overrightarrow{OM_{BC}} - \overrightarrow{OM_{AB}} = \left(\frac{15}2\ ,\ \frac{1}2\ ,\ 2\right)
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