Re: vector components and notation

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

> Sorry, John - but my email software did not properly
> translate your html code
> - odd, because the code looks fine. However, I could get the
> point of what you
> are saying. 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 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

which introduces unit vectors and the scalar components as usual.

Joel Rauber