1. The problem is: ( a x b )⋅[( b x c ) x ( c x a )] = [a,b,c]^2 = [ a⋅( b x c )]^2 I am supposed to solve this using index notation.... and I am having some problems. 2. Relevant equations: I guess I just don't understand the finer points of index notation. Every time I think I am getting it down I come back to this problem and get lost in the forest of letters. I am also still struggling with dummy vs free variables 3. The attempt at a solution: The most logical approach I thought would be to replace ( b x c ) = d and ( c x a ) = e giving me ( a x b )⋅( d x e ) = [a,b,c]^2 (Note: my instinct was to skip ahead to the 'end' but I think for the sake of learning I should show all my steps?) bold = vector ( a x b )⋅( d x e ) = aibjεijkek ⋅ dlemεlmpep = aibjdlemεijkεlmp(ek ⋅ ep) = aibjdlemεijkεlmpδkp = aibjdlemεijkεlmk = aibjdlem(δilδjm - δimδjl) = aibjdlemδilδjm - aibjdlemδimδjl = aibjdiej - aibjdjei Here is where I freeze up. Am I on the right track? Do I plug in for my values of d and e and keep hammering away? Whats the deal?