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

IfF= F1i+ F2j+ F3kandG= G1i+ G2j+ G3kare differentiable vector functions of (x,y,z) prove that div(F X G) = G·curl(F) - F·curl(G)

3. The attempt at a solution

If computed both sides of the equation, but they are not the same. My left hand side is

div(F X G) = (∂/∂x)(F2G3-G2F3) + (∂/∂y)(G1F3-F1G3) + (∂/∂z)(F1G2-F2G1)

My right hand side is

G·curl(F) - F·curl(G) = (∂/∂x)(2F2G3-2G2F3) + (∂/∂y)(2G1F3-2F1G3) + (∂/∂z)(2F1G2-2F2G1)

This weird two has appeared out of nowhere! I've checked over many, many times and still can't spot any arithmatic mistakes. I'll break it down below and hopefully somebody may be able to point out a mistake.

G·curl(F) = G1F3(∂/∂y) - G1F2(∂/∂z) - G2F3(∂/∂x) + G2F1(∂/∂z) + G3F2(∂/∂x) - G3F1(∂/∂y)

F·curl(G) = F1G3(∂/∂y) - F1G2(∂/∂z) - F2G3(∂/∂x) + F2G1(∂/∂z) + F3G2(∂/∂x) - G1F3(∂/∂y)

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# Homework Help: Proving div(F X G) = G·curl(F) - F·curl(G)

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