Need help with combination of dot product and cross product question

warfreak131

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

Let [tex]\vec{A}[/tex], [tex]\vec{B}[/tex], and [tex]\vec{C}[/tex] be three vectors which are all not in the same plane. Show that [tex]\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})[/tex]

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.

Pengwuino

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

warfreak131

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