# Vector Identity Rules Ax(BxC)

1. Aug 25, 2009

### omegacore

1. The problem statement, all variables and given/known data

Regarding the identity Ax(BxC)

2. Relevant equations

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

2. Aug 25, 2009

### 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 =)

3. Aug 25, 2009

### 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.

4. Aug 25, 2009

### queenofbabes

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

5. Aug 25, 2009

### Hurkyl

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

6. Aug 25, 2009

### kuruman

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

7. Aug 25, 2009

### Hurkyl

Staff Emeritus
Not all identities are universal. For example,
sin arcsin x = x​
is only valid on the interval $[-\pi/2, \pi/2]$.