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Re: i,j,k things.



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.