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Re: i,j,k things



Here's my spin:
There is nothing in the concept of a vector that requires it to have the
property of "dimensions", ie., it can be dimensionless - just a magnitude
and a direction.

If I divide the vector [10 m (due North)] by the dimensionless number 2, I
get the vector [5 m (due North)].
But if I divide the vector [10 m (due North)] by the dimensioned quantity
2m , I get the vector [5 (due North)] - a vector without dimensions - a
dimensionless magnitude plus a direction.

The voltage amplification of an electronic amplifier (expressed in Volts
per Volt) is a dimensionless scalar (just a number, without dimensions or
units). 5i is a dimensionless vector (just a vector, without dimensions
or units).
i is a dimensionless UNIT (magnitude = 1) vector; and all vector
operations (+, dot, cross) are applicable.

Bob

Bob Sciamanda (W3NLV)
Physics, Edinboro Univ of PA (em)
trebor@velocity.net
http://www.velocity.net/~trebor

"In the hard sciences we mostly talk about models rather than laws. And
if you talk to the people who are working on foundations of mathematics,
they also talk about models. It's certainly true of physics and astronomy
in particular that a law is just a model that we've got used to. . . . I
have enormous respect for Stephen Hawking, but I sometimes think he
doesn't know the difference between a model and the real thing. That's an
occupational disease of theoretical physicists." - Freeman Dyson in "A
Glorious Accident".