Re: i,j,k things.

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

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 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
would do what we already do with the common i,j,k notation
(long 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