The property is not valid for arbitrary vectors. It can only be right if a and b are perpendicular. The absolute value of a cross product is the product of the absolute value of the vectors times the absolute value of sin(phi), where phi is the angle between the vectors. So if the absolute value on both side of the identity is taken the right hand side shows |a|^2 |b| |sin(phi)| whereas the left side shows |a|^2 |b|
Raul Miller schrieb: > The cross product defined at > http://www.jsoftware.com/jwiki/Essays/Complete%20Tensor > seems to satisfy all the properties of cross product documented > at http://simple.wikipedia.org/wiki/Cross_product except the last. > > <math> \vec{a}\times(\vec{a}\times\vec{b}) = -|\vec{a}|^2\vec{b}</math> > > Is this a valid property for cross product? If not, why not? > If so, how do I interpret it in this context? > > Thanks, > > -- > Raul > ---------------------------------------------------------------------- > For information about J forums see http://www.jsoftware.com/forums.htm > > -- Prof. Dr. M. Schmidt-Gröttrup Hochschule Ulm, Fakultät Grundlagen Prittwitzstr. 10, 89075 Ulm E-Mail: [email protected] Tel: +49 (0) 731 50 28036 ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
