Triple Scalar Product

  • #1

Homework Statement



A x (B dot C)

(A x B) dot C

They are vectors.

Homework Equations



A x (B dot C)

(A x B) dot C

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?
 

Answers and Replies

  • #2
ehild
Homework Helper
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A x (B dot C)

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.

ehild
 
  • #3
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.

ehild

So would that mean I do A multiply by (B dot C)?
 
  • #4
SammyS
Staff Emeritus
Science Advisor
Homework Helper
Gold Member
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So would that mean I do A multiply by (B dot C)?
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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