- #1

- 204

- 7

## Homework Statement

Verify the identity:

## \nabla \times ( A \times B) = (B\bullet \nabla)A - (A\bullet\nabla)B + A(\nabla \bullet B)-B(\nabla\bullet A)##

My issue here is I don't understand the significance of why a term has B or A on the left of the dot product, and another has B or A on the right? (Eg ## B(\nabla)

Also, what is the significance of the ## \nabla ## being on the left, or right, of what it is multiplying? (Eg ## \langle \frac {d} {dx}, \frac {d} {dy}, \frac {d} {dz} \rangle \bullet \langle a_1, a_2, a_3 \rangle = \langle a_1, a_2, a_3 \rangle \bullet \langle \frac {d} {dx}, \frac {d} {dy}, \frac {d} {dz} \rangle##, or if the ## \nabla ## is on the right, does that leave the operator open to work on whichever comes AFTER the dot product?

## Homework Equations

## The Attempt at a Solution

I have my solution attached as a thumbnail, because it's pretty hefty.

Why does my solution look different than the given solution at the top?