Talk:Unit vector

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Is this algebra or geometry? I am not sure. Geometry guy 21:54, 20 May 2007 (UTC)

@ Charles Matthews: You are of course right if you say that the unit vector is not an identity of the multiplication, however it should be mentioned that it plays such a important role as does the null vector (which seems superflous for newcomers) because the unit vector is required to satisfy the rules of a mathemtical group and thus makes it an algebra in the first place. The same goes for the null vector. I would really appreciate it, if you could add this to both entries in terms that satisfy the otherwise strong mathemtical context, and i suppose you as a mathematican could do so best.--Slicky 11:40, Sep 17, 2004 (UTC)

Sorry, this really doesn't add up. There is no such thing as the unit vector, for one thing.

Charles Matthews 11:57, 17 Sep 2004 (UTC)

I am sorry i confused something. My bad. However regarding the null vector is should be mentioned that vector1 + null-vector = vector1 (thus the null-vector is the neutral element for the vector '+'-operation in a standard vector space). And because of that a group can be build (homogen, associative, neutral element, inverse element, commutative -> thus it is even abelian). Am I still mislead? I just deem it important to mention, because at first sight the null vector would seem a bit redundant.--Slicky 19:06, Sep 17, 2004 (UTC)

I think the null vector page now says that. Charles Matthews 19:12, 17 Sep 2004 (UTC)

Uhm,just saw it, i dunno what's gotten into me today. Its just that i am tired and a bit in a messy state. I apologize for that.

Good page. Clear and understandable, even to those without a doctorate in math. My interest is primarily in the use of coordinate cosines to describe ridgid body rotations in 3 dimensional space and the derivation of quaternions as used for the same purpose. SEIBasaurus.

[edit] Request for Expansion

I think it would be benificial to include unit vectors in the different coordinate systems (cylindrical, spherical, etc.). I'm not sure if this would be better suited for the coordinates page or not.

I think having a reference of curvilinear unit vectors and their properties (e.g. derivatives) would be especially helpful for those applying them to fields like electrodynamics and fluid mechanics.

I don't have a Ph.D, but I'm fairly fluent in vector calculus and could probably contribute more to the page. I just wanted to get some opinions and feedback first. RyanC. 19:46, 27 April 2006 (UTC)

Alright, I just ended up expanding the article myself. If anyone else frequents this page, let me know what you think.RyanC. 04:01, 1 May 2006 (UTC)

I took out the references to E&M when I rewrote since nothing here is specific to the field (pun unintentional). Lemme know (or just rewrite it better than I did) if I'm stepping on your toes too much. Eldereft 22:15, 26 May 2006 (UTC)

Good edits, I kind of got lazy and didn't bother to define the ranges of the variables. Looks good. I put the physics references in there because the only texts I've seen these coordinate systems used in were E&M and fluid dynamics. I haven't seen a math book on vector calculus that went into much depth at all about rotating coordinate systems. Then again I haven't read very many advanced texts on the subject. I've always been under the assumption that mathematicians worked primarily in Cartesian coordinates. Not really arguing the edits, mostly looking for feedback. Thanks. RyanC. 08:24, 30 May 2006 (UTC)

[edit] Notation

I'm actually kinda missing the $\hat{e}_x$ notation (or $\hat{e}_r$ , $\hat{e}_\phi$ , etc). Especially in physics where changes of coordinate system and the use of i and j for the imaginary unit (and/or current) can cause ambuguity, this is often used. I might add this myself (but feedback is appreciated of course) -- what I was actually wondering about is if it's not possible to make a dotless i, j, k to put the hat over. --CompuChip 09:54, 24 November 2006 (UTC)

On a related subject, I've seen in some (physics) books a-notation, where say the unit vector corresponding to the vector r becomes $\hat{a}_r$ . Is there any information on this subject somewhere? I can't find it in the article. Eudoxie (talk) 21:22, 13 February 2008 (UTC)

[edit] cylindrical coordinates

While I understand the geometrical meaning of $\boldsymbol{\hat{s}}$ and $\boldsymbol{\hat{z}}$ , I don't understand $\boldsymbol{\hat \phi}$ = $-\sin \phi\boldsymbol{\hat{x}} + \cos \phi\boldsymbol{\hat{y}}$ .

$\boldsymbol{\hat{s}}$ and $\boldsymbol{\hat{z}}$ relate to the length of their components, but an angle does not have a length. $\boldsymbol{\hat{\phi}}$ seems to be "90° ahead" of the angle it is describing. So what is it good for? --Abdull 10:10, 12 September 2007 (UTC)

Answer to myself: all three vectors form a orthogonal system. --Abdull 10:51, 12 September 2007 (UTC)

To clarify, the base vectors point in the direction of change. If you increase

φ

, the point will move in the direction indicated by $\hat\phi$ , likewise, if you increase r, the point will move in the direction indicated by $\hat{r}$ Eudoxie (talk) 21:26, 13 February 2008 (UTC)