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Math Help - Vectors

  1. #1
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    Vectors

    What can you conclude about a and b given that

    (a)  ||a||^2+||b||^2=||a+b||^2

    (b) ||a||^2+||b||^2=||a-b||^2

    I just do not like these open ended questions...I am never sure where to begin.
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  2. #2
    MHF Contributor Calculus26's Avatar
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    Recall u*u = ||u||^2

    ||a +b|| ^2 = (a+b)*(a+b) = ||a||^2 + 2a*b +||b||^2

    what does this tell you?
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  3. #3
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    One of the vectors is 0?
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  4. #4
    MHF Contributor Calculus26's Avatar
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    no a*b = 0

    what does this tell you ?
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  5. #5
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    Ohhh, they are perpendicular?

    (How does the second problem differ?)
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  6. #6
    MHF Contributor Calculus26's Avatar
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    you now know to answer that yourself.

    also it woud be a good time to reconsider what Captain Black had to say
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  7. #7
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    ||a-b||^2=(a-b)(a-b)=||a||^2-2ab+||b||^2

    I'm not sure how this differs from part (a) in that it just perpendicular vectors.

    I wasn't very clear on what captain black said about c=-b.
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  8. #8
    MHF Contributor Calculus26's Avatar
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    remember a - b is a + (-b)

    think about it --- consider the vectors i + j and i - j

    what is the difference between these 2?
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  9. #9
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    One vector is positive and one is negative?

    ||a+(-b)||^2=(a+(-b))(a+(-b))=a^2+2a(-b)+(-b)^2
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  10. #10
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    I'm not trying to sound rude but I have no idea what you are trying to say.
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  11. #11
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    Quote Originally Posted by Zocken View Post
    One vector is positive and one is negative?

    ||a+(-b)||^2=(a+(-b))(a+(-b))=a^2+2a(-b)+(-b)^2
    When c=-b

    ||a-b||^2=||a+c||^2

    and ||c||=||b||

    So now we are asking: What can you conclude when:

    ||a+c||^2=||a||^2+||c||^2

    and then what does that mean for a and b
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  12. #12
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    Does it mean b=0?

    or a>b?
    Last edited by Zocken; September 29th 2009 at 03:02 AM.
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  13. #13
    MHF Contributor Calculus26's Avatar
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    Does it mean b=0?

    or a>b?


    first of all vectors cannot be positive or negative. and it makes no sense

    to say things like a > b when and b are vectors.

    secondly the point i wanted you to see is that
    1. for both i + j and i - j |i+j|^2 = |i|^2 +|j|^2
    2. i an j are perpindicular
    3. If you graph the vectors notice that i , j and i+j form a right triangle

    as does i,j, and i - j which is the point Captain Black was making when he asked you to consider a parallelogram

    I think we were both trrying to get you to realize on your own with hints

    If
    a)

    (b)

    then a and b are perpindicular period.
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