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Math Help - 3 vectors has same magnitude

  1. #1
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    3 vectors has same magnitude

    hi
    I've tried to solve a problem which is saying that I've A,B and C are 3 vectors in R^3 and has a magnitude of 2 such that a+b+c=0 find the value of (a.b)+(b.c)+(a.c)

    first, A+B= -c

    so (A+B).C= 2 * 2* cos 180 = -4

    So A.C + B.C= -4

    and I've do so for A+c=-b

    so i got (A.b)+(b.c)= -4

    and I found that (A.B)= (A.C) i.e the angle between A and B is the same as the angle btwen A and C

    Anyway I can't go on from here. If that's right how can i get the last result . and if not .. please, tell me what is wrong
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  2. #2
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    Re: 3 vectors has same magnitude

    Quote Originally Posted by ahmedzoro10 View Post
    hi
    I've tried to solve a problem which is saying that I've A,B and C are 3 vectors in R^3 and has a magnitude of 2 such that a+b+c=0 find the value of (a.b)+(b.c)+(a.c)
    HINT:
    C\cdot C=4 so A\cdot C+B\cdot C+4=0

    Do that twice more using B~\&~A. Then add.
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  3. #3
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    Re: 3 vectors has same magnitude

    Quote Originally Posted by Plato View Post
    HINT:
    C\cdot C=4 so A\cdot C+B\cdot C+4=0

    Do that twice more using B~\&~A. Then add.
    Still unreachable , sorry
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  4. #4
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    Re: 3 vectors has same magnitude

    I've got that

    A.c + B.c+C.c=0
    A.b+b.c+b.b=0
    a.b+A.c+a.a=0
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  5. #5
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    Re: 3 vectors has same magnitude

    Quote Originally Posted by ahmedzoro10 View Post
    Still unreachable , sorry
    I am not going to complete the problem for you.
    This is the last hint I will give.
    \begin{array}{l} A \cdot C + B \cdot C =  - 4 \\  A \cdot B + B \cdot C =  - 4 \\  A \cdot B + A \cdot C =  - 4 \\  \end{array}

    You want A \cdot B + B \cdot C + A \cdot C = ?
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  6. #6
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    Re: 3 vectors has same magnitude

    OMG!! I've reached this equations 2 hrs ago but I was like a drunk.

    Thanks alot
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