Proof of a Relation Between Cross Product and Dot Product

This comes from an extra-credit question in my math class. 

Prove: \( \vec a \times (\vec b \times \vec c) = (\vec a * \vec c)\vec b - (\vec a * \vec b)\vec c \)

I can prove it alternatively by manipulating the components algebraically with determinant calculations, but such an approach doesn't make any intuitive sense, and after all, it's boring.

How I edit math equations

The Area Under a Parabola and the Volume of a Pyramid

This is a sketch of an idea I had in 2017. At the time, I didn't know the technical details of calculus but only had an understanding of its philosophy.