Perhaps this is not the kind of example that was intended, but it seems to
me we can state a vector via its components by only partially specifying the
coordinate system, and educated people will correctly choose an appropriate
system and use it.
Example, At an ice-covered intersection a 750-kg car with velocity +15 m/s i
collides with a 900-kg car with velocity 18 m/s j. As a result of the
collision the cars become stuck together. Find the velocity of the cars
immediately after the collision.
I have not specified a 2-dimensional Cartesion coordinate system, but that
will be assumed by the educated reader. I have not specified whether the
i-direction is east or north or 20-degrees north of east or whatever, but it
does not matter. I have not specified a right-handed system, but that does
not matter. All the reader has to assume to get the same answer I got is to
assume that i and j are orthogonal.
Michael D. Edmiston, Ph.D. Phone/voice-mail: 419-358-3270
Professor of Chemistry & Physics FAX: 419-358-3323
Chairman, Science Department E-Mail edmiston@bluffton.edu
Bluffton College
280 West College Avenue
Bluffton, OH 45817