(adsbygoogle = window.adsbygoogle || []).push({}); 1. The problem statement, all variables and given/known data

The vectorsFandGare arbitrary functions of position. Starting w/ the relationsFx (∇ xG) andGx (∇ xF), obtain the identity

∇(F.G) = (F. ∇)G+ (G. ∇)F+Fx (∇ xG) +Gx (∇ xF)

2. Relevant equations

3. The attempt at a solution

I started off with the relationFx (∇ xG) and used the BAC-CAB rule:

Fx (∇ xG) = ∇(F.G) - (G. ∇)F

so ∇(F.G= (G. ∇)F+Fx (∇ xG) which seems to contradict the identity I am supposed to get. What am I doing wrong?

**Physics Forums | Science Articles, Homework Help, Discussion**

Dismiss Notice

Join Physics Forums Today!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

# Obtaining vector identities

**Physics Forums | Science Articles, Homework Help, Discussion**