Griffiths' Introduction to Electromagnetism -book has equations called 20.10 below.
I have proved this equation d) pretty much on the first mathematics -course I had but I have not yet understood a visual way to remember it. How can I visually explain it? Why does it have a negative sign?
$$\bar a\times (\bar b\times\bar c)=\bar b (\bar a\cdot\bar c)-\bar c (\bar a\cdot \bar b)$$