- #1

fatpotato

- Homework Statement
- Prove the relation ##\nabla \cdot (A \times B) = B \cdot (\nabla \times A) - A\cdot (\nabla \times B)##

- Relevant Equations
- Definition of the vector product, definition of the divergence.

Majoring in electrical engineering imply studying Griffiths book on electrodynamics, so I have begun reading its first chapter, which is a review of vector calculus. A list of vector calculus identities is given, and I would like to derive each one, with one of them being ##\nabla \cdot (A \times B) = B \cdot (\nabla \times A) - A\cdot (\nabla \times B)##.

Now, I have two questions about this :

Thank you.

Now, I have two questions about this :

- Methodology question : I have seen a lot of threads here on PF about deriving these identitites, and Einstein's summation notation and Levi-Civita symbol are mentioned every time. Given that I will be majoring in electrical engineering and not in physics, can a mere engineer learn these notations or does this involve higher unreachable mathematical concepts?
- Actual question about the identity : I have seen an identity ##A \cdot (B \times C) ## involving a determinant, but since ##\nabla## is an operator and not an actual vector, does it even make sense to use the identity?

Thank you.