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Math Help - Check properties of dot product problem

  1. #1
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    Check properties of dot product problem

    Check please. Just need to make sure I am doing this right.

    Given  \vec{u}\cdot\vec{u}=8,\;\vec{v}\cdot\vec{v}=6,\; \vec{u}\cdot\vec{v}=7

    Find: (3u-v)\cdot (u-3v)

    (3u-v)\cdot (u-3v)\implies \\(3u-v)\cdot u-[(3u-v)\cdot 3v]\implies \\3u\cdot u-v\cdot u-[3u\cdot 3v-v\cdot 3v]\implies \\3(u\cdot u)-v\cdot u-9(u\cdot v)+3(v\cdot v)\implies \\3(8)-7-9(7)+3(6)\implies \\(3u-v)\cdot (u-3v)=-28
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  2. #2
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    Re: Check properties of dot product problem

    Quote Originally Posted by emccormick View Post
    Check please. Just need to make sure I am doing this right.
    Given  \vec{u}\cdot\vec{u}=8,\;\vec{v}\cdot\vec{v}=6,\; \vec{u}\cdot\vec{v}=7
    Find: (3u-v)\cdot (u-3v)
    (3u-v)\cdot (u-3v)\implies \\(3u-v)\cdot u-[(3u-v)\cdot 3v]\implies \\3u\cdot u-v\cdot u-[3u\cdot 3v-v\cdot 3v]\implies \\3(u\cdot u)-v\cdot u-9(u\cdot v)+3(v\cdot v)\implies \\3(8)-7-9(7)+3(6)\implies \\(3u-v)\cdot (u-3v)=-28
    Yes that is correct. But note that it is easier to see

    (3\vec{u}-\vec{v})\cdot(\vec{u}-3\vec{u})=3\vec{u}\cdot\vec{u}-10\vec{u}\cdot\vec{v}+3\vec{v}\cdot\vec{v}
    Last edited by Plato; May 5th 2013 at 01:42 PM.
    Thanks from emccormick
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  3. #3
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    Re: Check properties of dot product problem

    Thanks. Thought it was, but no solutions to the even ones. Whee.
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