Need help with combination of dot product and cross product question

Homework Statement

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

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.

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Pengwuino
Gold Member
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

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