Vector Product

matqkks

Given two vectors p and q, why is the vector (cross) product pxq perpendicular to the plane containing these vectors?
Is there a geometric or physical way of explaining why?
Are there any real life examples we can draw from?

Landau

Well, what is your definition of cross product? Sometimes this (perpendicularity) is part of the definition.

Rasalhague

Two links posted recently in these forums are online introductions to multivariable calculus which each contain a chapter relating the algebraic expression for the components of a cross product to the property of being perpendicular to its factors:

http://synechism.org/drupal/cfsv/
http://www.owlnet.rice.edu/~fjones/

Greg Egan used to have a nice demonstration of the correspondence between geometric and componentwise definitions of the dot product (which is taken as the starting point by the links above), but I can't seem to find it now. Never mind, Google knows lots more. You can shop around for the one that makes most sense to you.