# How can I prove it?

1. Oct 31, 2009

### rado5

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

How can I prove this theorem? A, B, C and D are vectors.

(A$$\times$$B).(C$$\times$$D)=(A.C)(B.D)-(A.D)(B.C)

2. Relevant equations

A$$\times$$B=ABsin($$\theta$$) and A.B=ABcos($$\theta$$)

3. The attempt at a solution

Please help me solve it.

2. Oct 31, 2009

### aPhilosopher

There's one more relevant equation. As a hint, think of AxB as an additional vector V.

3. Oct 31, 2009

### VeeEight

4. Oct 31, 2009

### rado5

yeah I'm sure that this solves the problem, and it seems obvious, so thank u very much, but do u know an easier way or a cleaner (lol) way to prove it.

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