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Homework Help: Triple Scalar Product

  1. Feb 8, 2012 #1
    1. The problem statement, all variables and given/known data

    A x (B dot C)

    (A x B) dot C

    They are vectors.

    2. Relevant equations

    A x (B dot C)

    (A x B) dot C

    3. The attempt at a solution

    I know how to do my homework, but I am confused on these formulas.

    Is the first formula "A x (B dot C)" the same as the second one? I know the second one is the same as
    A dot (B x C).

    It doesn't make sense to me. Wouldn't the B dot C become a scalar? So how could A cross with that?
  2. jcsd
  3. Feb 8, 2012 #2


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    Homework Helper

    The first multiplication is not "cross product". The dot product of two vectors is a scalar, and the cross product is defined for two vectors. What you wrote is just a product of A with a scalar.

  4. Feb 8, 2012 #3
    So would that mean I do A multiply by (B dot C)?
  5. Feb 8, 2012 #4


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    Staff Emeritus
    Science Advisor
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    Gold Member

    The scalar triple product of for vectors A, B, and C is a combination of a cross-product (also called a vector-product) and a dot-product (also called a scalar-product) .

    It's only defined if you do the cross product first.

    (A×B)∙C and A∙(B×C) are both defined.

    Neither (ABC nor A×(BC) is defined if × denotes the vector product. It's not possible to form a cross-product with a vector and a scalar.
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