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-----Original Message-----
From: John Mallinckrodt [mailto:ajm@CSUPOMONA.EDU]
Sent: Wednesday, September 18, 2002 9:25 AM
To: PHYS-L@lists.nau.edu
Subject: Re: vector components and notation
Joel Rauber wrote:
John Mallinkrodt wrote:*magnitude* of
> If there is a vector indicated by <bold>A</bold>_sub_x, then
> <italic>A</italic>_sub_x should formally represent the
> that vector and, thus, would never have a negative valueas it could
> if it instead represented the scalar x-component of the vector
> <bold>A</bold>.
I'm not sure I follow:
Agreed. See below.
let me restate and clarify the notation that Ivector quantities
believe is consistant
(Small note: I'm a proponent of arrows over letters for
instead of boldfacing. But I'll follow what you have doneabove for ASCII
clarity.)
Ditto
<bold>A</bold> = a vector
<bold>A_x</bold> = a component vector, John D's projection onto
<bold>i_hat</bold>
A_x = a scalar component = <bold>A</bold> dot <bold>i_hat</bold>
|A_x| = a positive scalar, the length of the component vector
<bold>A_x</bold>
It does appear that I am still failing to make my point.
I'll try once more:
By convention we write
|<bold>A</bold>| = magnitude of the vector <bold>A</bold>
but we generally allow ourselves the notational shortcut
A = |<bold>A</bold>|
In other words, when a textbook writes a quantity in bold face, it is
understood to be a vector and when that *same quantity* is written in
regular (but usually italicized) face, it is understood to represent
the *magnitude* of the vector which is always *nonnegative* quantity.
Thus, if we allow ourselves to refer to the vector
<bold>A_x</bold>
then, logically, the quantity
|<bold>A_x</bold>| = A_x
represents the *magnitude* of *that* vector and shouldn't *also* be
used to represent the scalar x_component of the (different) vector
<bold>A</bold>
To avoid this ambiguity, I simply prefer never to use the notation
<bold>A_x</bold>
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
Pomona, CA 91768-4031 office:Building 8, Room 223