- #1
JordanD
- 7
- 0
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. Homework 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 variables3. 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?
( 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. Homework 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 variables3. 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?