mammothrob

04-27-2007, 06:21 PM

Im trying to prove this identity.

Let u v and w be vectors in (Rn) and <u,u> denote the dot product.

u x ( v x w ) = <u,w> v - <u,v> w

Here are my ideas on this.

I tried using the normal algebraic properties of the cross product... dead end.

My next idea is to just prove it for (R3)

Let u = (u1, u2, u3) v= w = and so on, and just plug it in on the left side and try to find the right.

If that does work, could I assume that it will work for (Rn), becuase pluging in u = (u1, u2, u3...un) for each vector seems crazy.

Any ideas or other ways to prove this one? Not looking for the proof just a place to start.

Rob

Let u v and w be vectors in (Rn) and <u,u> denote the dot product.

u x ( v x w ) = <u,w> v - <u,v> w

Here are my ideas on this.

I tried using the normal algebraic properties of the cross product... dead end.

My next idea is to just prove it for (R3)

Let u = (u1, u2, u3) v= w = and so on, and just plug it in on the left side and try to find the right.

If that does work, could I assume that it will work for (Rn), becuase pluging in u = (u1, u2, u3...un) for each vector seems crazy.

Any ideas or other ways to prove this one? Not looking for the proof just a place to start.

Rob