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Math Help - Vector Product

  1. #1
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    Vector Product

    Dear all,

    I have a vector identity and am confused about the notation

    <br />
\bf a\times (\bf b\times \bf c)=\bf b(\bf a\cdot \bf c)-\bf c(\bf a\cdot\bf b)<br />

    where \bf a, \bf b and \bf c are vectors and \times and \cdot are the cross and dot product respectively.

    My question is what is the operation between \bf b(a?

    It isn't the dot product. Is it the scalar product? Also is it commutative?

    <br />
\bf b(\bf a\cdot \bf c)-\bf c(\bf a\cdot\bf b)=(\bf a\cdot \bf c)\bf b-(\bf a\cdot\bf b)\bf c<br />
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  2. #2
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    Quote Originally Posted by davefulton View Post
    Dear all,

    I have a vector identity and am confused about the notation

    <br />
\bf a\times (\bf b\times \bf c)=\bf b(\bf a\cdot \bf c)-\bf c(\bf a\cdot\bf b)<br />

    where \bf a, \bf b and \bf c are vectors and \times and \cdot are the cross and dot product respectively.

    My question is what is the operation between \bf b(a?

    It isn't the dot product. Is it the scalar product? Also is it commutative?

    <br />
\bf b(\bf a\cdot \bf c)-\bf c(\bf a\cdot\bf b)=(\bf a\cdot \bf c)\bf b-(\bf a\cdot\bf b)\bf c<br />

    The only possible, and sensical, meaning of b(a\cdot c) is the vector b multiplied by the scalar a\cdot c ...Now you prove this.

    Tonio

    Pd. I'm assuming you're working with vectors in \mathbb{R}^3...?
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  3. #3
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    The dot product of any two vectors is a scalar. This answers my question. Thank you. I suppose this implies it is commutative also.
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  4. #4
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    Quote Originally Posted by davefulton View Post
    The dot product of any two vectors is a scalar. This answers my question. Thank you. I suppose this implies it is commutative also.

    Well, the product of a scalar and a vector is obviously commutative, as is the dot product, but NOT the cross product!

    Tonio
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