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Vector identity proof

  • Thread starter Lunat1c
  • Start date
  • #1
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Homework Statement



Hi. I need to prove that [b x c, c x a, a x b] = [a, b, c]2 for any three vectors a, b and c.

Note that [a, b, c] = a(b x c)


Homework Equations



I tried using the identify (a x b) x c = (a.c)b - (a.b)c

The Attempt at a Solution



Using the above identity I got [b x c, c x a, a x b] = (b x c){(c x a) x (a x b)} = (b x c){(a(a x b)a - (ca)(a x b)}. I'm not sure where to go from here or if it's the correct approach at all

Thanks for any help!
 

Answers and Replies

  • #2
CompuChip
Science Advisor
Homework Helper
4,302
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If a, b, c are vectors, then (b x c) is a vector. So then, what does the multiplication a(b x c) mean? Is it inner product of a with (b x c)? Are the vectors three dimensional?
Or are you working in a Clifford algebra where ab is the Clifford (geometrical) product and x is the commutator product (b x c = 1/2(bc - cb)).
 

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