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Re: [Phys-L] closed vectors



It seems to me that if three or more unit vectors are not identical, then they are inevitably closed (= form a closed figure) if they occur in a plane. I expect that the concept of unit vector or "direction" has meaning in arbitrary numbers of dimensions, and so for however many unit vectors it is easy to imagine each having extension in a different dimension, hence being open. So much for directions describing a closed figure. But the question was presented as directions closed when crossed.
What can I understand by "crossed"? If this is taken to mean cross-product or vector product, then as usually understood, this is restricted to three dimensions and is normal to the plane of the directions, taken two at a time. But as is the way of mathematicians and others with an interest, such vectors can be generalized to n dimensions. Interesting to see that for some situations only spaces with three or seven dimensions have meaning.
But that is more than enough stream of consciousness from someone who is innocent of any background in the field.

Brian Whatcott

On 10/6/2014 1:32 PM, Paul Lulai wrote:
Hello.
I am working through some problems and came upon a question I need some help with.
I have some basic unit vectors and I am asked if the set of unit vectors are closed when crossed.
It's been a while.
>From what I recall, closed simply means the vectors would create an enclosed shape.
- is this a correct interpretation?
- if not, could you clarify?

I have no recollection of why this knowledge would be helpful for dot or cross products. Since it was asked, I imagine I am missing something.
- what am I missing (I assume quite a bit here)?

Thanks for any insight you can provide.
Have a good one.
Paul.
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