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Re: vector components and notation



Joel Rauber wrote:

I rather like the use of the vectors A_x and A_y, as they provide a nice
geometric approach to introducing the idea of components. One has probably
just finished defining vector addition geometrically (head-to-tail and
parallel transport). Its then natural to define component vectors as those
unique vectors parallel to the coordinate axes that add up to the vector A.

One can then write:

A_x vector = (A_x) i_hat etc

As John Denker mentioned, this may be just fine for us since we can
interpret what was *meant*. But students already have enough trouble
distinguishing between vectors, magnitudes of vectors (which are
nonnegative scalars), and components of vectors (which are signed
scalars.) They don't need us to make their lives even harder by
using inconsistent notation.

If there is a vector indicated by <bold>A</bold>_sub_x, then
<italic>A</italic>_sub_x should formally represent the *magnitude* of
that vector and, thus, would never have a negative value as it could
if it instead represented the scalar x-component of the vector
<bold>A</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