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Math Help - Norm of Vectors

  1. #1
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    Norm of Vectors

    I feel like this is a really stupid question but I just can't figure out how to solve it:

    If ||u|| = 2 and ||v|| = and u (dot) v = 1, find ||u (dot) v||

    Thanks for the help!

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  2. #2
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    Quote Originally Posted by Laydieofsorrows View Post
    I feel like this is a really stupid question but I just can't figure out how to solve it:

    If ||u|| = 2 and ||v|| = and u (dot) v = 1, find ||u (dot) v||

    Thanks for the help!

    It's not stupid but something's wrong here: both the dot product and the norm are defined for vectors (the first one for two, the second one for one) and give back a scalar (a number), so ||u (dot) v|| is the norm of a scalar, not a vector, and this doesn't make much sense. Read carefully the question again.

    Tonio
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    I checked the problem and it's correct.

    Can I get another opinion?
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  4. #4
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    Quote Originally Posted by Laydieofsorrows View Post
    I checked the problem and it's correct.

    Can I get another opinion?


    I suppose you can get a million opinions yet the question still makes no sense as given. If you're not giving all the data then do.

    Tonio
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  5. #5
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    Quote Originally Posted by Laydieofsorrows View Post
    I checked the problem and it's correct.

    Can I get another opinion?
    You can trust tonio, he's an expert. Seriously, if the question is as stated then either it's a trick question or there's a mistake in it. If the norm of a scalar means anything at all, then it must just mean the absolute value. So if u (dot) v = 1, then ||u (dot) v|| = 1.
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  6. #6
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    Is it possible that the problem asked for ||u\times v||, the norm of the cross product of u and v?

    If so, you could use the facts that |u \cdot v|= ||u||||v||cos(\theta) and ||u\times v||= ||u||||v|| sin(\theta), where \theta is the angle between u and v.

    Since you are given that |u\cdot v|= 1 as well as the values of ||u|| and ||v||, you can solve for cos(\theta). Use that to find \theta (which must be between 0 and \pi) and then find sin(\theta).
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