Re: vector components and notation

["RAUBER, JOEL" <JOEL_RAUBER@SDSTATE.EDU>]

This is also not a big deal to me, but the notation I have advocated,
similar to Serway's isn't that far off from Halliday and Resnick.

Halliday and Resnick refer to "component vectors" as well, denoting them
(they use arrows as well as bolding for vector quantities.

a_x <hat>i</hat>

Serway simply goes the next step to give this vector a single symbol, namely

<arrow>a_x</arrow>

H&R have a name for this concept of "component vector", use the concept;
they just don't provide a single symbol (consistant with other symbology)
for it.  Serway does.

Having said this, I'm happy leaving the notation for the X-component vector
of <bold> a </bold> as

a_x <hat>i</hat>



While we are here, I notice inconsistant use of the terminology
"projection".

The projection of <bold>A</bold> on <bold>i_hat</bold> according to some
authors means

<bold>A</bold> dot <bold>i_hat</bold> = A_x

and according to others (John D. in his post for example)

( <bold>A</bold> dot <bold>i_hat</bold> ) * <bold>i_hat</bold> =
<bold>A_x</bold>

Joel Rauber

> -----Original Message-----
> From: John Mallinckrodt [mailto:ajm@CSUPOMONA.EDU]
> Sent: Tuesday, September 17, 2002 9:02 PM
> To: PHYS-L@lists.nau.edu
> Subject: Re: vector components and notation
>
>
> Bob LaMontagne wrote:
>
> > ... Yes, Serway does use the two vectors Ax and Ay - however, he is
> > careful not to use the word "component" until he actually
> defines the term
> > from the scalar lengths of those vectors. Then he drops the
> vectors Ax and Ay
> > completely throughout the remainder of the text and only uses scalar
> > components. I think his presentation could have been even
> stronger by leaving
> > out those two vectors entirely - I think that was your
> objection and I agree
> > with you. Do you have favorite textbooks that you feel take a clearer
> > approach? ...
>
> This is not a very big deal with me but, since you ask, I guess I
> tend to favor what seems to me the traditional approach as
> exemplified by Halliday, Resnick, and Krane (or some permutation
> thereof) and other texts which limit themselves to using vectors,
> scalar components of vectors, and unit vectors.  I would prefer a
> textbook that indicates vectors the way we actually write them (i.e.,
> as non-bold face characters with arrows over the top) and that
> indicate unit vectors using non-bold face characters like x, y, and z
> with "hats" (rather than bold face i, j, and k.)
>
> John
> --
>     A. John Mallinckrodt        http://www.csupomona.edu/~ajm
>     Professor of Physics      mailto:ajm@csupomona.edu
>     Physics Department         voice:909-869-4054
>     Cal Poly Pomona              fax:909-869-5090
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