How to Prove the Identity ∇×(u×v)=v∙∇u-u∙∇v+u∇∙v-v ∇∙u?

[oxxiissiixxo]

Can any show me how you will go about proofing this identity

∇×(u×v)=v∙∇u-u∙∇v+u∇∙v-v ∇∙u where v and u are vectors

Many thanks.

 

[GOBIND]

IT IS VECTOR TRIPLE PRODUCT EXPANSION

SIMPLY SOLVE IT BY EXPANDING DEL
AND APPLY IT TO FIRST VECTOR AND TAKING SECOND(VECTOR) CONSTANT AND THEN VICE VERSA.

U SHOULD ALSO ASSUME GENERAL DIFFIRENT FORMS OF VECTORS IN (I,J,K).

U SHOULD ALSO CHECK THE SCALAR AND VECTOR FORMS ,i.e,"X" & "." IS APPLIED B/W TWO VECTORS(WHICH GIVE AGAIN A VECTOR & SCALAR RESP.)

OR U SHOULD PREFER A GOOD BOOK.

 

[HallsofIvy]

Gobind, thank you for your post but please take off your Caps lock!

oxxiissiixxo, as Gobind says, the simplest way to prove that is probably to go ahead and doing the calculations. Tedious but not difficult.