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Math Help - Help finding a vector given two vectors?

  1. #1
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    Help finding a vector given two vectors?

    Help finding a vector given two vectors?-math.png


    Find the values of x and y and write vector B.

    xi+yj * 4i + 2j = -16

    How do I find x and y?
    Last edited by INeedOfHelp; November 12th 2012 at 12:18 PM.
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  2. #2
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    Re: Help finding a vector given two vectors?

    Equate the dot product of A and B to -16, and to what should you equate the dot product of B and C?

    Once you write these products, then you will two equations in x and y.
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  3. #3
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    Re: Help finding a vector given two vectors?

    So...

    (yj)(2j)+(xi)(4i)= -16
    2yj2+4xi2 = -16

    So far is that right, or no?
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  4. #4
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    Re: Help finding a vector given two vectors?

    I would write:

    \vec{A}\cdot\vec{B}=\langle 4,2 \rangle \cdot \langle x,y \rangle=4x+2y=-16\,\therefore\,2x+y=-8

    Now, since \vec{B} and \vec{C} are perpendicular, to what will we equate their dot product?
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  5. #5
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    Re: Help finding a vector given two vectors?

    B C
    <2,1> * <2,3> = (4)+(3) = 7
    That's not right, is it?
    hdfhkfdg
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  6. #6
    MHF Contributor MarkFL's Avatar
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    Re: Help finding a vector given two vectors?

    No, that's not right...you are taking the dot product of one half of A and C...you want to use B and C, and set it equal to what?
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    Re: Help finding a vector given two vectors?

    Equal to 0 because they are orthogonal vectors??
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  8. #8
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    Re: Help finding a vector given two vectors?

    Yes, exactly...good. So what equation results from this?
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    Re: Help finding a vector given two vectors?

    2x+3y=0 ?
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    MHF Contributor MarkFL's Avatar
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    Re: Help finding a vector given two vectors?

    Great! Now, you have:

    (1) 2x+y=-8

    (2) 2x+3y=0

    Solve this system to get x and y.
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  11. #11
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    Re: Help finding a vector given two vectors?

    So would vector B = <-6,4> ?
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  12. #12
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    Re: Help finding a vector given two vectors?

    Yes, great work!
    Thanks from INeedOfHelp
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  13. #13
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    Re: Help finding a vector given two vectors?

    Thank you so much! (:
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