Thread: The nabla operator and vector calculation rules

1. The nabla operator and vector calculation rules

Hi

This is a very short question that I need to understand in order to get a better understanding of vector identities proofs.

Is (B dot nabla)A the same as B(nabla dot A) ?

Im currently working on proofs using the nabla operator and einsteins eidi method and it's very hard as I have little to no directions on the matter from my university course.

While im at it, I also wonder if
(B dot nabla)AC is the same as C(B dot nabla)A. I always tend to get all my vectors outside my paranthesis to one side rather than one on each side, which they have on the answers in my book.

I thank anyone who can shed some ligth on this!

Regards
/Hanga

2. Re: The nabla operator and vector calculation rules

Originally Posted by Hanga
This is a very short question that I need to understand in order to get a better understanding of vector identities proofs.
Is (B dot nabla)A the same as B(nabla dot A) ?
Lets be clear on the notation.
By nabla I assume you mean the del operator.
$\displaystyle \nabla = i\frac{\partial }{{\partial x}} + j\frac{\partial }{{\partial y}} + k\frac{\partial }{{\partial z}}$
Is that correct?

If so what sort of functions are $\displaystyle A~\&~B~?$

P.S. This is a good reference.

3. Re: The nabla operator and vector calculation rules

Argh, I wrote a reply but I got some error.

A and B are vectors with continous derivatives so it wont ever become 0.
The link is very good, but im still quite unusre about how to solve my second question. From what i've gathered from your link, it's more important on what vector the del operator is acting on and everything around this operation can be put anywhere. Am I thinking right on this matter?

,

nabla operator rules

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