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Math Help - Let U=... V=... Find ||...||

  1. #1
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    Let U=... V=... Find ||...||

    Let
    U=
    |-1|
    |2 |
    |1 |

    V=
    |3 |
    |1 |
    |-1|

    Find:

    || [1/(||U-V||)](u-v)||

    Starters?

    Thanks in advance
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  2. #2
    A Plied Mathematician
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    You can compute that expression without doing any numerical computations, if you use some of the properties of norms, such as || av || = |a| ||v||. Does this give you some ideas?
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  3. #3
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    What can you say about the length of \frac{\vec{v}}{||\vec{v}||}?
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  4. #4
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    Need more help

    I don't get it...please explain more

    Thanks
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  5. #5
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    You would agree that

    \dfrac{1}{\|u-v\|} is a scalar, right? And it's positive?

    So

    \left\|\dfrac{1}{\|u-v\|}(u-v)\right\|=\left\|\dfrac{1}{\|u-v\|}\right\|\,\|u-v\|=\dots?
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  6. #6
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    If v is a nonzero vector then \left\| {\dfrac{v}<br />
{{\left\| v \right\|}}} \right\| = 1
    That is all there is to it.
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  7. #7
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    So does it end up being = 1? because you times the thing up.?
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  8. #8
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    Well, I don't know what you mean by "times the thing up". You have a/a, where a is not zero. That's always 1.
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  9. #9
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    Why don't you know the basic properties of the norm function?
    If \alpha is a scalar and v is a vector then \left\| {\alpha v} \right\| = \left| \alpha  \right|\left\| v \right\|.

    Therefore \left\| {\dfrac{v}{{\left\| v \right\|}}} \right\|=\left| {\frac{1}{{\left\| v \right\|}}} \right|\left\| v \right\| = \frac{1}<br />
{{\left\| v \right\|}}\left\| v \right\| = 1
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  10. #10
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    Because I am a high school student trying to learn University alg by using a text book that doesn't teach anything.
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  11. #11
    A Plied Mathematician
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    Technically, it's \|u-v\|/\|u-v\|=1.

    Be careful with your parentheses!
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