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Math Help - Vectors proof

  1. #1
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    Vectors proof

    I have got nowhere with this question: Non-zero non-parallel vectors a, b and c are such that b x c = c x a. Prove that a + b = kc for some scalar k.
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  2. #2
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    Re: Vectors proof

    Quote Originally Posted by Stuck Man View Post
    I have got nowhere with this question: Non-zero non-parallel vectors a, b and c are such that b x c = c x a. Prove that a + b = kc for some scalar k.
    By the given we know that \vec{c}\times(\vec{b}\times \vec{c})=\vec{c}\times(\vec{c}\times \vec{a})

    But \vec{c}\times(\vec{b}\times \vec{c})=(\vec{c}\cdot\vec{c})\vec{b}-(\vec{c}\cdot\vec{b})\vec{c}

    Now expand the RHS and solve for \vec{a}+\vec{b}.
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  3. #3
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    Re: Vectors proof

    I had not used the vector triple product before. I think I have done this now.
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