Question

ques

Answer 1

For a vector triple product, we have
\[\textbf a \times (\textbf b \times \textbf c)=(\textbf a.\textbf c)\textbf b-(\textbf a.\textbf b)\textbf c\]
then why is
\[\vec \nabla \times (\vec A \times \vec B)=(\vec \nabla.\vec B)\vec A-(\vec \nabla.\vec A)\vec B+(\vec B .\vec \nabla)\vec A-(\vec A.\vec \nabla)\vec B\]
Does this imply
\[(\vec B.\vec \nabla)\vec A=(\vec A.\vec \nabla)\vec B\]