Re: [Phys-L] closed vectors

[Jeffrey Schnick <JSchnick@Anselm.Edu>]

> -----Original Message-----
> From: Phys-l [mailto:phys-l-bounces@www.phys-l.org] On Behalf Of Roger
> Haar
> Sent: Monday, October 06, 2014 2:51 PM
> To: Phys-L@Phys-L.org
> Subject: Re: [Phys-L] closed vectors
>
> Hi,
>      "Closed"  implies that the cross product any members of the set is in the
> original set of unit vectors.
>
> For example if your original set contains only the unit vector x and y, the
> question becomes is the cross product of x and y in the original set of unit
> vectors.  It is not because
>
> x  CROSS y  is  z.
>
> And z is not in the original set.
>
> If your origin set of unit vectors was x, y, and z, the set would be closed with
> respect to cross products. (At least up to a minus sign)

I would say that the set of the three Cartesian unit vectors and their negatives is not closed with respect to the cross product operator because any one of them crossed into itself is 0 which is not one of the 6 elements of the set.
 
> Thanks Roger
>
>
>
>
> On 10/6/2014 11:32 AM, 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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