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Math Help - Equality of products.

  1. #1
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    Equality of products.

    I'm sorry if this has been asked, I've searched around and couldn't find it.

    a + b + c = 0

    where a, b and c are vectors.

    Q) Show that a*b = b*c = c*a

    Thanks.
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  2. #2
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    Are you using an asterix to represent dot product, cross product, componentwise multiplication, or something else entirely?
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  3. #3
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    If you mean dot product, this isn't true, Take a to be a unit vector, b= -a, c= 0. Then a\cdot b= |a|^2= 1 while a\cdot c= b\cdot c= 0.

    If you mean the cross product, it still isn't true. Take a= \vec{i}, b=-\vec{i}+ \vec{j} and c= -\vec{j}. Then a\times b= b\times c= \vec{k}, but a\times c= -\vec{k}.

    So what does "*" mean?
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  4. #4
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    It could be the cross product. The last product is c times a, not the other way around.

    Edit: And if it is the cross product, you may find it useful to write c = -a-b.

    You then need to check that b*c and c*a are both equal to a*b (recall that the cross product is linear in both variables (like any good product), and that x*x=0 for all x).
    Last edited by HappyJoe; May 6th 2011 at 08:31 AM. Reason: Adding math.
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  5. #5
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    i was referring to the cross product, sorry if I wasn't clear enough :L
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  6. #6
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    Have you solved the problem yet?
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  7. #7
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    How many dimensions are the vectors?
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  8. #8
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    @Prove It, It doesn't state how many dimensions but I'm assuming 3? Not entirely sue

    @HappyJoe Thanks for all your help your explanation helped me, as well as @HallsofIvy's example.

    Thanks again guys I've got it
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  9. #9
    Member HappyJoe's Avatar
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    Good.
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