Talk:Lists of vector identities

Thanks. I've been trying to learn TeX and this is how I'm doing it. I know some purists might not appreciate that.

People don't know what this is just by looking at it. A couple sentences exposition would help.-LtNOWIS 04:44, 6 Apr 2005 (UTC)

I changed Green's first identity because the notation was incorrect. All these are the same:

$\left({{\vec {\nabla }}{\rm {f}}\cdot {\vec {\nabla }}{\rm {f}}}\right)=\left[{{\frac {\partial f}{\partial x}},{\frac {\partial f}{\partial y}},{\frac {\partial f}{\partial z}}}\right]\cdot \left[{{\frac {\partial f}{\partial x}},{\frac {\partial f}{\partial y}},{\frac {\partial f}{\partial z}}}\right]=\left({\frac {\partial f}{\partial x}}\right)^{2}+\left({\frac {\partial f}{\partial y}}\right)^{2}+\left({\frac {\partial f}{\partial z}}\right)^{2}=\left\|{{\vec {\nabla }}{\rm {f}}}\right\|^{2}$

but

$\left({{\vec {\nabla }}{\rm {f}}}\right)^{2}$

doesn't exist, and

${\vec {\nabla }}{\rm {f}}^{2}=\left[{{\frac {\partial f^{2}}{\partial x}},{\frac {\partial f^{2}}{\partial y}},{\frac {\partial f^{2}}{\partial z}}}\right]=2f\left[{{\frac {\partial f}{\partial x}},{\frac {\partial f}{\partial y}},{\frac {\partial f}{\partial z}}}\right]=2f{\vec {\nabla }}{\rm {f}}$

is something completely different. Joaoliveira 31-aug-2006 20:00 UTC

Changed back the 2nd cross in

$\nabla \times ({\vec {A}}\times {\vec {B}})={\vec {A}}\times (\nabla \times {\vec {B}})-{\vec {B}}\times (\nabla \times {\vec {A}})-({\vec {A}}\times \nabla )\times {\vec {B}}+({\vec {B}}\times \nabla )\times {\vec {A}}$

but I'm still not convinced it's correct, can't find a source for it anywhere else. Badgerific (talk) 14:41, 3 March 2009 (UTC)[reply]

Hello ... I have extended the article "Vector calculus identities" by adding a few more identities. Now, I think this article is subset of the other article!. So, I would like to suggest to delete(or something equivalent) the article "List of vector identities". If anybody has objection, please let us discuss. zinka 09:29, 5 May 2010 (UTC)