How can Lagrange Identity be used to prove a vector equation?

[Ahmedzica]

Homework Statement

Prove that (A x B) . (u x v) = (a.u) (b.v) - (a.v)(b.u)

The Attempt at a Solution

I've used lagrange indentity to proof that. but I can't go ahead

Thanks

 

[MathematicalPhysicist]

Patience is a virtue here.

I guess you know already that the LHS equals to:
det((AxB)1 (AxB)2 (AxB)3 ; u1 u2 u3 ; v1 v2 v3)

and that (AxB)i= Aj Bk - Ak Bj for a suitable cyclic order.
Now calculate the determinant.

afterward calculate explicitly the RHS.

There's no other way, you need to get your hand dirty.