bac-cab rule

The bac-cab rule states that for vectors$𝐀$, $𝐁$, and$𝐂$ (that can be either real or complex) in ${ℝ}^3$, we have

$$𝐀\times (𝐁\times 𝐂)=𝐁(𝐀\cdot 𝐂)-𝐂(𝐀\cdot 𝐁).$$

Here $\times$ is the cross product, and $\cdot$ is the real inner product.