Re: [Phys-l] bound vectors ... or not

["Jeffrey Schnick" <JSchnick@Anselm.Edu>]

Last I checked the calculus book used at my college is Calculus by James
Stewart, 6th Ed. Thomson, Brooks/Cole.  I see it listed at several web
sites as a best seller.  In the following quotes, letters representing
vectors should be in boldface and CD should have an arrow over it.  I
have omitted boldface used for emphasis by Stewart.  In section 13.2 it
states:

"The term vector is used by sientists to indicate a quantity (such as
displacement or velocity or force) that has both magnitude and
direction."
Later on:
"The corresponding displacement vetor v, shown in Figure 1, has initial
point A (the tail) and terminal point B (the tip)  ..."
"Notice that the vetor u = CD has the same length and the same direction
as v even though it is in a different position.  We say that u and v are
equivalent (or equal) and we write u = v"

---------------

I think of a vector as a mathematical entity with magnitude and
direction that transforms under coordinate transformations in a
prescribed manner.

Magnitude and direction are inherent properties of a vector.  We
associate vectors with physical quantities that have magnitude and
direction as inherent properties.  Just as an object can have inherent
properties and relational (to the rest of the universe) properties such
as position and velocity, the physical quantity associated with a vector
can have the relational property of position (point of application)
relative to some point in space, e.g. one that we designate as the
origin of a coordinate system. In our speech we often refer to the
physical quantity represented by a vector as a vector itself.  And
clearly at least some of us use words that lump the relational property
of a vector in with its inherent properities and call the totality a
fixed/bound vector or a sliding vector.  If we consider a vector to have
only magnitude and direction, and that the turns of phrase making
positional information part of the vector are simply (very common) loose
speech used for conciseness at the expense of accuracy, are these turns
of phrase dangerous in the sense that they cause or exasperate
misconceptions?

Note that I think of the electric field in some region of space as the
association of a vector with each point in space in that region.  I
don't think of the position of the point in space or the point in space
itself as being part of the vector.


> -----Original Message-----
> From: phys-l-bounces@carnot.physics.buffalo.edu [mailto:phys-l-
> bounces@carnot.physics.buffalo.edu] On Behalf Of brian whatcott
> Sent: Monday, September 06, 2010 12:46 PM
> To: phys-l@carnot.physics.buffalo.edu
> Subject: Re: [Phys-l] bound vectors ... or not
>
>   When I searched Google scholar for [bound vector] it was important
to
> select 'exact phrase' in the search options, and explicitly exclude
> 'upper lower', else cites with   ' lower or upper  bound..vector'
> occured too often.
> Of the 206 cites remaining, this concept is still mixed with other
> concepts: but still,   it seems that it is  folks working in optics
who
> are more apt to use the concept in connection with electromagnetics.
>   Schrodinger, the  soliton and the super-heavy flavor show up.  And
> engineering texts, of course.
>
> Brian W
>
> On 9/6/2010 8:14 AM, treborsci@verizon.net wrote:
> > One might say that a vector field (e.g. the electric field E(r,t) )
> defines
> > a vector (E) associated with, "located at", (or "bound to") each
> space-time
> > point.
> > It seems that Faraday extended this view to reification.
> >
> > Bob Sciamanda
> > Physics, Edinboro Univ of PA (EM)
> > treborsci@verizon.net
> > http://mysite.verizon.net/res12merh/
> >
> > --------------------------------------------------
> > From: "John Denker"<jsd@av8n.com>
> > Sent: Sunday, September 05, 2010 1:04 PM
> > To: "Forum for Physics Educators"<phys-l@carnot.physics.buffalo.edu>
> > Subject: [Phys-l] bound vectors ... or not
> >
> > > In the wikipedia article on "the vectors mainly used in physics
> > > and engineering" it talks about "free vectors" and "bound vectors".
> > >   http://en.wikipedia.org/wiki/Euclidean_vector
> > >
> > > This came as a surprise to me.  I am 99.99% certain the
> > > notion of "bound vector" does not appear in any of my math
> > > books.  I don't recall seeing it in any of my physics books.
> > > I don't recall hearing any physicist utter the term or use
> > > the concept.
> > > . . .
>
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