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Ignoring zero, one can say that a scaler is represented by either a positive or a negative number. Likewise, ignoring boundaries, one can say that the ending of a 2D vector is in one of the four quadrants. For a 3D dimensional vector the ending of a vector (the tip of the arrow) is in one of the eight "regions."
Replacing the word "region" by "quadrant" is not acceptable. What word should I use?
Ludwik
http://csam.montclair.edu/~kowalski/life/intro.html