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Re: components



From: Hugh Haskell <hhaskell@MINDSPRING.COM>

That should be doable. different vectors don't have to be
components
of a third one. They don't even have to be related. Two
velocities of
different objects can be combined to yield various relative
velocities. Force and displacement can be combined to
yield work.
Etc. None of this has to be done in the context of a
particular
coordinate system, although it is often more convenient to
do so. You
can think about the dot product as the magnitude of the
projection of
one vector on the other, divided by the magnitude of the
vector
projected upon. The magnitude of a cross product is the
area of the
parallelogram formed by the two vectors, and the triple
product is
the area of the parallelopiped formed by the three
vectors. None of
these things requires that a coordinate system be defined,
although
lots of geometric things that are well handled by
coordinate systems
are formed by combinations of vectors--two vectors define
a plane
(unless they are colinear). If a third no-coplanar vector
is added
that defines a three-dimensional space.

I would think what you want to do can be done, but what is
it going
to get you? Why not embrace the coordinate systems and
show that any

It's the approach taken in Matter & Interactions. It's made
me think about things I've never been made to think about
before.

Sign conventions are giving me trouble. Sometimes neg signs
show up as direction indicators and sometimes they simply
mean "oppositely directed".




Cheers,
Joe

CVAC Home Page <http://users.vnet.net/heafnerj/cvac.html>
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