Need help with combination of dot product and cross product question

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

Let $$\vec{A}$$, $$\vec{B}$$, and $$\vec{C}$$ be three vectors which are all not in the same plane. Show that $$\vec{A}{\cdot}(\vec{B}{\times}\vec{C})=\vec{B}{\cdot}(\vec{C}{\times}\v ec{A})=\vec{C}{\cdot}(\vec{A}{\times}\vec{B})$$

2. Relevant equations

Don't know :(

3. The attempt at a solution

Well I looked up some algebraic properties of dot products and cross products, but nothing that relates the two. I tried working it out, but it's getting extremely messy.
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 Recognitions: Gold Member You're actually proving a common property of dot products and cross products. You can just work it out by brute force, but the way I was taught back in the day is by index notation which is described here: http://www.physicsforums.com/showthread.php?t=198712
 thank you, but that link is really complicated and i dont understand it. as for brute force, that would be so long and tedious, and the probability of making a minor error which results in an incorrect answer is so high is there any easier way to do it? EDIT: nevermind, I got it, brute force worked, thanks