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Re: i,j,k things



Unit vectors are as much vectors as any. I teach my students that a
unit vector can be created from any vector by dividing the vector by its
magnitude. The magnitude of a unit vector is dimensionless, a pure
number, equal to one irrespective of the "units" of the original
vector. Also, the scalar product of any unit vector with itself is one,
e.g., i dot i = 1; j dot j = 1; n dot n = 1; etc.

IMHO, referring to vectors such as i, j, k, n as unit vectors is
appropriate and sensible.

Glenn A. Carlson, P.E.
St. Charles County Community College
St. Peters, MO
gcarlson@mail.win.org

Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU> wrote:
Subject: i,j,k things.
Date: Fri, 17 Sep 1999 23:36:31 -0400
From: Ludwik Kowalski <KowalskiL@MAIL.MONTCLAIR.EDU>

If we agree that in physics the term "unit" refers to things
such as kg, m/s and N, then the term "unit vector" is
probably not appropriate for i, j and k.

Let me elaborate. First, i, j and k are dimensionless,
otherwise they could not be used for so many different
physical quantities. (In F=3i+4j the unit, N, goes with
the scalars 3 and 4, not with i and j.) Second, the
dimensionless quantities, such as v/c, are scalars;
the operation of division does not apply to vectors
pointing in different directions.

So what does the word "unit vector" mean? One unit
of what? F=1j is a vector whose length is 1 N, and
which is directed along the y axis. Likewise F=1i is
a vector. But i and j alone are not vectors. A vector
quantity may have many different directions; j is
always pointing along the +y axis.

I am not proposing to change anything. Only to
recognize that the word "unit" means a different
thing here. Would you agree? We multiply scalars
by i, j and k in order to create vectors. What would
be a better name for i, j and k?
Ludwik Kowalski