Message-Id: <v01540b0cb0bf4f6577f6@[192.174.2.173]>
Date: Thu, 18 Dec 1997 14:13:36 -0800
To: pinhole@exploratorium.edu
From: pauld@exploratorium.edu (Paul Doherty)
Subject: Re: Vectors
A quantity with a magnitude and direction need not be a vector.
Consider rotation of a book. The rotation has an direction about which the
book is rotated and a magnitude how many degrees. But vectors must have the
proprty that they add commutatively. Vectore A plus vector B = vector B +
vector A.
Consider rotating the book about a nail driven though the center of the
cover by 90 degrees clockwise.
and rotating the book about a nail slipped into the middle of the open edge
of the book with the point toward the spine by 90 degrees clockwise (as you
look down the nail)
Apply these operations in two diferent orders: the book starts the same and
ends up different. Therefore these two things with magnitude and direction
are not vectors.
Paul Doherty