Help with a linear algebra rule

Hello,

Can anyone help to identify the name of this linear algebra rule:

Quote:

|A, B, C| = -(A cross C) dot B = -(C cross B) dot A

If it doesn't have a name, can anyone briefly tell me what it does or how it works or where should I look for an explanation, thank you very much.

Re: Help with a linear algebra rule

It's called a triple scalar product.

Re: Help with a linear algebra rule

And it is NOT from "linear algebra". The cross product is defined only in $\displaystyle R^3$, not in a general finite dimensional vector space.