On 29 April 2010 22:35, Raul Miller <[email protected]> wrote: > <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?
In general, it is not. a×(a×b) is perpendicular to both a×b and a, which means that it is in the plane of a and b. More precisely, b and a×(a×b) are in the opposite half-planes w.r.t. a – this uniquely determines a×(a×b)'s direction. The magnitude of a×(a×b) is a²|b|·|sin(a,b)|. It follows that a×(a×b)=-a²b only holds when a⊥b. ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
