## Is there a notation for unit vectors?

For the discussion of math. Duh.

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Qaanol
The Cheshirest Catamount
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### Is there a notation for unit vectors?

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?
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z4lis
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### Re: Is there a notation for unit vectors?

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.
What they (mathematicians) define as interesting depends on their particular field of study; mathematical anaylsts find pain and extreme confusion interesting, whereas geometers are interested in beauty.

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

^ (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

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

Kow wrote:^ (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

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

jestingrabbit
Factoids are just Datas that haven't grown up yet
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### Re: Is there a notation for unit vectors?

Derek wrote:
Kow wrote:^ (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

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

Derek wrote:
Kow wrote:^ (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

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: $\inline \mathbf{\hat v } = {\ll \mathbf{v} \gg} = u(\mathbf{v}) = unit(\mathbf{v}) = {\mathbf{v} \over \left \| \mathbf{v} \right \|}$

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

Flumble wrote:
Luckily, with math, everything is defineable:

Oh really? http://en.wikipedia.org/wiki/Definable_real_number
*whistle*