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### Is there a notation for unit vectors?

Posted: **Sun Aug 31, 2014 2:30 am UTC**

by **Qaanol**

I want a simple way to indicate symbolically, “u is a unit vector in the direction of (long formula)”. The straightforward way is u = (long formula) ÷ |long formula|, which is rather cumbersome. I’d much rather have something to the effect of u = «long formula» that would mean the same thing.

For example, say I want the unit vector in the direction of the projection of x onto the orthogonal complement of y. The orthogonal part of x is p = x - (y÷|y|)(x•(y÷|y|)), so the result I want is p÷|p|. I’d prefer to be able to write something like «x - «y»(x•«y»)».

Does such a notation already exist?

### Re: Is there a notation for unit vectors?

Posted: **Sun Aug 31, 2014 2:39 am UTC**

by **z4lis**

There's nothing wrong with using the notation <<x>> to denote the unit vector in the direction of x, as long as you're clear that's what you're doing.

### Re: Is there a notation for unit vectors?

Posted: **Sun Aug 31, 2014 3:34 am UTC**

by **Kow**

^ (hat) the term I learned in classes and is the symbol that the Wikipedia article on unit vectors uses as well.

http://en.wikipedia.org/wiki/Unit_vector

### Re: Is there a notation for unit vectors?

Posted: **Sun Aug 31, 2014 5:51 am UTC**

by **Derek**

Hat doesn't really work well over long terms, it's mostly used over single variables.

### Re: Is there a notation for unit vectors?

Posted: **Sun Aug 31, 2014 11:47 am UTC**

by **jestingrabbit**

Derek wrote:Hat doesn't really work well over long terms, it's mostly used over single variables.

yeah, but you can just call your big formula something, and then hat that. Although if you do that, you may as well, not worry about hat and use x/|x|.

Of course, if you're doing this a couple of times, you could define a function, unit, but that's as clumsy as my other suggestions.

### Re: Is there a notation for unit vectors?

Posted: **Sun Aug 31, 2014 1:15 pm UTC**

by **Flumble**

Derek wrote:Hat doesn't really work well over long terms, it's mostly used over single variables.

If you can give us an example of a long term that isn't better off mapped to a variable (in this context of course), please do.

Luckily, with math, everything is defineable:

### Re: Is there a notation for unit vectors?

Posted: **Tue Sep 02, 2014 11:30 am UTC**

by **Farabor**

Flumble wrote:

Luckily, with math, everything is defineable:

Oh really?

http://en.wikipedia.org/wiki/Definable_real_number*whistle*