Show that A·(B×C) = B·(C×A) = C·(A×B)

[warfreak131]

Homework Statement

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

Homework Equations

Don't know :(

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:

https://www.physicsforums.com/showthread.php?t=198712

 

[warfreak131]

thank you, but that link is really complicated and i don't 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