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Math Help - vector question2

  1. #1
    Senior Member euclid2's Avatar
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    vector question2

    given

    vector U=(1,3,-2)
    vector V=(-2,2,2)
    vector W=(5,1,4)

    demonstrate that vectors u,v, and w are all perpendicular to each other.

    i took the dot product u dot v, v dot w, and u dot w and they all came to be 0.

    is this complete after three dot products prove to be 0 demonstrating they are all perpendicular?
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  2. #2
    A Plied Mathematician
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    Your work is sufficient to prove the result, yes.
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  3. #3
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    \vec{u}\cdot\vec{v}= |\vec{u}||\vec{v}| cos(\theta) where \theta is the angle between them. If neither vector is the 0 vector and their dot product is 0 then we must have cos(\theta)= 0. Since \theta must be between 0 and 180 degrees, that means \theta must be 90 degrees- the two vectors are perpendicular.
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