Is Divergence Commutative in Vector Calculus?

[Pythagorean]

is (DEL dot A) the same as (A dot DEL)?

I know the dot product is commutative, but this involves an operator.

if the answer is YES, than why does one of the product rules read like this:

DEL X (A X B) = (B dot DELL)A - (A dot DEL)B + A(DEL dot B) - B(DEL dot A)

they commute the operator with its operand.

if the answer is NO, than what is the relationship between (DEL dot A) and (A dot DELL)?

this is not a homework question.

 

[Pythagorean]

Oh... it's called the convective operator for anyone interested... I tried so many different combinations in google

http://mathworld.wolfram.com/ConvectiveOperator.html