## Iner product

Triple product expansion
Main article: Triple product

This is a very useful identity (also known as Lagrange’s formula) involving the dot- and cross-products. It is written as

$\mathbf{a} \times (\mathbf{b} \times \mathbf{c}) = \mathbf{b}(\mathbf{a}\cdot\mathbf{c}) - \mathbf{c}(\mathbf{a}\cdot\mathbf{b})$

which is easier to remember as “BAC minus CAB”, keeping in mind which vectors are dotted together. This formula is commonly used to simplify vector calculations in physics.

Nhiều tính chất khác tại http://en.wikipedia.org/wiki/Cross_product
It is not associative, but satisfies the Jacobi identity:

$\mathbf{a} \times (\mathbf{b} \times \mathbf{c}) + \mathbf{b} \times (\mathbf{c} \times \mathbf{a}) + \mathbf{c} \times (\mathbf{a} \times \mathbf{b}) = \mathbf{0}.$