(adsbygoogle = window.adsbygoogle || []).push({}); 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

[tex](\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)[/tex]

2. Relevant equations

I believe that he is somehow using the rule that

[tex]\mathbf{A}\times(\mathbf{B}\times\mathbf{C}) = \mathbf{B}(\mathbf{A}\cdot\mathbf{C}) - \mathbf{C}(\mathbf{A}\cdot\mathbf{B})\qquad(2)[/tex]

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?

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

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