# Homework Help: (AxB).(CxD) = ?

1. May 4, 2010

1. The problem statement, all variables and given/known data

I am following along in a book and in one line the author asserts that

$$(\mathbf{A}\times\mathbf{B})\cdot(\mathbf{C}\times\mathbf{D}) = (\mathbf{A}\cdot\mathbf{C})(\mathbf{B}\cdot\mathbf{D}) - (\mathbf{A}\cdot\mathbf{D})(\mathbf{B}\cdot\mathbf{C})\qquad(1)$$

2. Relevant equations

I believe that he is somehow using the rule that

$$\mathbf{A}\times(\mathbf{B}\times\mathbf{C}) = \mathbf{B}(\mathbf{A}\cdot\mathbf{C}) - \mathbf{C}(\mathbf{A}\cdot\mathbf{B})\qquad(2)$$

3. The attempt at a solution

Is this the only rule he is using to arrive at (1) ?
I am having trouble see how to implement this to arrive at the same result. Am I missing something painfully obvious?

2. May 4, 2010

Did you try to do this in terms of components, i.e. using the definition of the cross and dot product? (Didn't try it myself, only suggesting.)

Edit: although it might get a little messy...

3. May 4, 2010

### rock.freak667

I would think they'd use this formula as well as this one

$$A\cdot (B \times C) = B \cdot (C \times A) = C \cdot (A \times B)$$

4. May 4, 2010