Understanding the Triple Scalar Product in Vector Calculus

[brotivation]

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?

 

[ehild]

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

 

[brotivation]

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)?

 

[SammyS]

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 (A∙B)×C nor A×(B∙C) is defined if × denotes the vector product. It's not possible to form a cross-product with a vector and a scalar.