Vector Triple Product


a x (b x c) = b(a.c) - c(a.b)

In words, that's a vector in the plane spanned by b and c, taking as
its weight in b the projection of a on c, times the magnitude of c,
and as the weight in c minus the projection of a on b, times the
magnitude of b.

Now... what the hell does that mean intuitively, and just what is its
physical application?

(BTW, is there proof of this identity simpler than expanding in
components?)

.

Relevant Pages

  • Re: Vector Triple Product
    ... its weight in b the projection of a on c, times the magnitude of c, ... Vector c can be written as a component along b (unit vector 1_b) ...
    (sci.physics)
  • Re: Are we heavier at night?
    ... OK,great, plenty of theories. ... (Well, not quite, those who predict some change in weight should at ... least *try* to predict the magnitude). ... Notice, no ad hominum arguments, just calculations are required now. ...
    (sci.physics)
  • Re: Are we heavier at night?
    ... (Well, not quite, those who predict some change in weight should at ... least *try* to predict the magnitude). ... Notice, no ad hominum arguments, just calculations are required now. ...
    (sci.physics)
  • Re: Vector Triple Product
    ... its weight in b the projection of a on c, times the magnitude of c, ... Presumably, writing down the relevant forumla for an extended body, using the inertia tensor instead of a mass-point, it may be possible to generate terms of the form a x ...
    (sci.physics)
  • Re: Vector Triple Product
    ... its weight in b the projection of a on c, times the magnitude of c, ... Since a x is also orthogonal to a, the dot product with ... Vector c can be written as a component along b (unit vector 1_b) ...
    (sci.physics)