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Math Help - Simplifying Cross Products

  1. #1
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    Simplifying Cross Products

    Hi guys

    I'm boggled by this problem

    a x (b x (a x b))

    I know the first step is to simplify the triple vector product inside the () which leads this expression

    a x (( b dot b)a - (b dot a)b)

    but the book claims that the final answer is eventually

    (- a dot ba x b)

    Can someone explain why?
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  2. #2
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    Quote Originally Posted by gotpho View Post
    Hi guys

    I'm boggled by this problem

    a x (b x (a x b))

    I know the first step is to simplify the triple vector product inside the () which leads this expression

    a x (( b dot b)a - (b dot a)b)

    but the book claims that the final answer is eventually

    (- a dot ba x b)

    Can someone explain why?
    Expand your first step

     <br />
b \cdot b \left( a \times a\right) - a \cdot b \left( a \times b\right)<br />

    noting that a \times a = 0.
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  3. #3
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    Never knew you could distribute like that

    But isn't a dot a = |a|^2. How do you know that they are orthogonal?
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  4. #4
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    Quote Originally Posted by gotpho View Post
    Never knew you could distribute like that

    But isn't a dot a = |a|^2. How do you know that they are orthogonal?
    I believe it's a \times a not a \cdot a.
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  5. #5
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    Quote Originally Posted by Danny View Post
    I believe it's a \times a not a \cdot a.
    Oh, my bad. Thanks.
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