I Understanding the Vector Triple Product Proof

[Decimal]

Hello,

I am having trouble understanding a proof presented here:

http://www.fen.bilkent.edu.tr/~ercelebi/Ax(BxC).pdf

This is a proof of the triple product identity, but I don't understand the last step, where they calculate $\lambda$. Don't you lose all generality when you state $\vec A$ equals $\vec C$?

Thanks!

 

[Orodruin]

No. You do not loose any generality. The number $\lambda$ is a constant that should be independent of what vectors you use. Hence, it is perfectly fine to use $\vec A = \vec C$. When you do this you get a relation for $\lambda$, but $\lambda$ is independent of what the vectors actually are. Hence, since it is equal to one for a particular choice of vectors, it must be equal to one for any choice of vectors.

 

[Decimal]

Ah I see, for some reason I interpreted the $\lambda$ to be dependent on the choice of vectors, but of course there is no reason for doing so. Thanks a lot!