Proof - Vector Calculus - Curl

[cristina89]

I need to prove this: u x (\nabla x u) = \frac{1}{2}\nabla(u²) - (u \cdot \nabla)u.

I've came to this: uj∂iuj - uj∂jui (i think it's correct)
But how this 1/2 appears?

 

[tiny-tim]

welcome to pf!

hi cristina89! welcome to pf!

(try using the X₂ button just above the Reply box )

I need to prove this: u x (\nabla x u) = \frac{1}{2}\nabla(u²) - (u \cdot \nabla)u.

I've came to this: uj∂iuj - uj∂jui (i think it's correct)
But how this 1/2 appears?

'cos ∂_i(u_ju_j)= 2u_j∂_i(u_j)