Re: i,j,k things

[Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>]

RESENDING WHAT I THINK WAS LOST.
Ken Caviness wrote:

> .... But the thread continues -- much to my surprise, so I'll
> jump in after all. ...

Let me do the same. Suppose that instead of F=2i-3j we use a
different notation, for example, F=(2,-3,0), where positions are
significant. There are no unit vectors here, only a reference to
an existing set of axes, and to units, such as N or V/m. (Scalar
components of a vector must always be in the same units.) To
add two vectors we wouold add their corresponding component
while to find the dot product we would multiply the corresponding
components, and add the products. For a cross product we could
do what we already do with the common i,j,k notation (a set of
position-sensitive expressions in proper order).

Physics with positional notation for vectors would not be more
difficult than physics with notation based on the i,j,k labels. It is
only a matter of book keeping, as emphasized earlier by another
contributor. Yes, we do turn i, j,k into vectors when we write,
for example, E=(2V/m)i-3(V/m)j but that should not prevent me
from saying that all by themselves i,j,k are notational symbols
which facilitate book keeping. Yes, components of a vector are
vectors. And yes, as stated by Robert Carlson, a unit vector is
created by dividing a vector by its magnitude.

The common practice of solving problems in terms of unit
vectors is working well and a distinction between vectors
(1i, 1j,1k) and symbols (i,j,k) is not necessary, except in
academic debates about meanings of things.
Ludwik Kowalski