Question

ques

Answer 1

\[\vec \nabla \times \vec \nabla \times \vec f=\vec \nabla(\vec \nabla . \vec f)-\nabla^2 \vec f\]
Can we use vector triple product to prove this identity??Expanding it is long and unecessary :/

Answer 2

are you familiar with the Ricci's symbol

Answer 3

Nope

Answer 4

you can apply this identity:
\[\Large {\mathbf{a}} \times \left( {{\mathbf{b}} \times {\mathbf{c}}} \right) = \left( {{\mathbf{a}} \cdot {\mathbf{c}}} \right){\mathbf{b}} - \left( {{\mathbf{a}} \cdot {\mathbf{b}}} \right){\mathbf{c}}\]

Answer 5

that's what I am asking if it's ok to use that

Answer 6

It looks like a quick and cheat method lol

Answer 7

yes! you have to memorize that identity :)

Answer 8

alright sweet :D

Answer 9

:)

Answer 10

do it!!

you're just pattern matching after all and \(\nabla\) is functionally a vector....

Answer 11

yeah :P