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From: Hugh Haskell <hhaskell@MINDSPRING.COM>components
That should be doable. different vectors don't have to be
of a third one. They don't even have to be related. Twovelocities of
different objects can be combined to yield various relativeyield work.
velocities. Force and displacement can be combined to
Etc. None of this has to be done in the context of aparticular
coordinate system, although it is often more convenient todo so. You
can think about the dot product as the magnitude of theprojection of
one vector on the other, divided by the magnitude of thevector
projected upon. The magnitude of a cross product is thearea of the
parallelogram formed by the two vectors, and the tripleproduct is
the area of the parallelopiped formed by the threevectors. None of
these things requires that a coordinate system be defined,although
lots of geometric things that are well handled bycoordinate systems
are formed by combinations of vectors--two vectors definea plane
(unless they are colinear). If a third no-coplanar vectoris added
that defines a three-dimensional space.it going
I would think what you want to do can be done, but what is
to get you? Why not embrace the coordinate systems andshow that any
It's the approach taken in Matter & Interactions. It's made