How is this proof valid? ax(bxc) = (c.a)b-(b.a)c

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The discussion centers on the validity of a proof for the vector triple product, specifically the equation ax(bxc) = (c.a)b - (b.a)c. The user initially struggles with a mismatch in terms during the proof's final part, questioning the correctness of their notation and vector representation. They highlight a specific discrepancy between terms in the two expressions. Ultimately, the user resolves the issue after a friend points out that a term was missing in the ax(bxc) calculation. The conversation emphasizes the importance of careful notation and term inclusion in vector proofs.
mr_coffee
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Hello everyone, I'm looking at this proof and its making sense until the very last part, and it doens't friggin' work...the terms don't match up... Also is the notation I used correct in the proof, like does there have to be any vector notation I don't have or do you see anyhting you don't like? I'm proving the "The Vector triple product"
Here is my proof:
http://img89.imageshack.us/img89/9758/rpooof6rk.jpg
Look at the 2nd part of ax(bxc) -----> a1b1c3 - a2b22c3 + a2b3c2
then look at the last part (c.ad)b - (b.a)c ---> a1b3c1 - a1b1c3 + a2b3c2 - a2b2c3

You see only 1 term isn't match up! the a1b1c3 not equal to a1b3c1 what's going on? Thanks
 
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Nevermind, my friend found the problem! I forgot a term in ax(bxc) part.
 
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