- #1
Destroxia
- 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?