What is the validity of the vector identity Ax(BxC)?

[omegacore]

Homework Statement

Regarding the identity Ax(BxC)

Homework Equations

Does this identity only hold when A != B != C?

 

[queenofbabes]

Which identity are you referring to? Whatever the identity it would work for any vector...but of course the cross product of 2 equal vectors is zero =)

 

[omegacore]

Ah yes, I forgot the identifying portion of the identity:

Ax(BxC) = B(A dot C) - C(A dot B)

Same qualifying question as before. Obviously this identity does not just fall out of the sky and is the product of a process. I am wondering if the process is disrupted (invalid identity) by having A = B... it seems like it wouldn't be.

 

[queenofbabes]

No it wouldn't, I wonder what makes you think so?

 

[Hurkyl]

It's fair to wonder, because some sources tend to be somewhat sloppy about explicitly stating hypotheses.

 

[kuruman]

An identity holds for any choice of vectors. That's what makes it an "identity".

 

[Hurkyl]

Not all identities are universal. For example,

sin arcsin x = x​

is only valid on the interval $[-\pi/2, \pi/2]$.