# Homework Help: Difference between dS and ds̄

1. Dec 1, 2011

### TranscendArcu

Difference between "dS" and "ds̄"

http://img268.imageshack.us/img268/126/skjermbilde20111201kl71.png [Broken]

I often see theorems such as the one above in my coursework, but I do not actually understand the difference between "dS" and "ds̄". I presume, because the latter has a "hat," that the latter also has something to do with vectors. So what's the difference between these two differential distances?

Last edited by a moderator: May 5, 2017
2. Dec 1, 2011

### Staff: Mentor

Re: Difference between "dS" and "ds̄"

The dS on the left is a vector, an increment of some vector S (looks sort of like the integral for work). The one on the right has dS as a scalar. The integrand here is the dot product of two vectors, which results in a scalar.

Last edited by a moderator: May 5, 2017
3. Dec 1, 2011

### Ray Vickson

Re: Difference between "dS" and "ds̄"

$d\vec{S}$ is the vector whose direction is $\vec{n}$ and whose magnitude is $dS$, so, in fact, we have $$d\vec{S} = \vec{n} dS.$$

RGV