@johnny09 This is related to Lagrange's formula: $$\vec a \times (\vec b \times \vec c) = \vec b (\vec a \cdot \vec c) - \vec c (\vec a \cdot \vec b).$$

Wikipedia: Triple product

Some related posts on the main site: Do the BAC-CAB identity for triple vector product have some intepretation?, Correct scaling factor in Lagrange's formula for triple cross product. (The second one is my question.)

It three vectors are linearly independent, then the triple product $\vec a\cdot (\vec b\times \vec c)$ is non-zero.

However, the triple vector product $\vec a\times (\vec b\times \vec c)$ can be zero. Just consider $\vec i \times (\vec j\times \vec k)$.

@MartinSleziak Thanks! I'll take a look on what you shared! :)