Re: i,j,k things.

[Joel Rauber <Joel_Rauber@SDSTATE.EDU>]

Michael's comments are very appropos, with the following proviso.

> Once we have said that, then i,j,k become defined vectors.
> The "thing"
> called i has direction (along the x axis) and it has length (length of
> one along a newton scale).  I believe this is sufficient to make it a
> vector... it has magnitude and direction.
All it takes to be a
> vector is
> to be something that requires both magnitude and direction to specify
> it.

It requires more than magnitude and direction to be a vector quantity.  The
best counter example are finite rotations in 3d space.  They may be
represented by a magnitude (number of radians rotated) and a direction (use
of right-hand-rule is how one can do it).  And yet such quantities are not
vectors, since they do not obey the usual rules of vector addition, e.g.
they don't add in a communitive sense.  Perhaps a better statement is to say
that a vectors have magnitude and directions and are quantities that combine
together in the same way as displacement vectors; that is, have the same
algebra.  BTW, I'm assuming we are talking about vectors in a Euclidean
Space; if not things get more complicated.

i,j,k have the above properties, of course.

For further reference see: "Teaching Introductory Physics" by Clifford
Swartz and Thomas Miner, chapter 3, page 79.

For the record, I don't follow their advice to *not* introduce unit vectors
in introductory physics classes.

> By the way, I agree that the units (m, N) of a vector specified using
> unit (magnitude-one) vectors go with the scalar and not with the unit
> vector.  Unit vectors themselves are dimensionless.

I don't think it matters where you associate the unit and view it as a
matter of preference; de gustubus non est desputandum  (sp?)

Joel Rauber

> Michael D. Edmiston, Ph.D.