characteristics of vector product
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There are several algebraic properties of vector product. Here are the main among them:
1. anticommutativity: [a,b] = -[b,a]
2. distributive property: [a,(b+c)] = [a,b] + [a,c]
3. associativity: [(f a),b] = [a,(f b)] = f [a,b]
4. vector triple product: [a,[b,c]] = b(ac) - c(ab)
5. [a,a] = 0
6. [[a,b],c] + [[b,c],a] + [[c,a],b] =0
7. mixed triple product: ([a,b] c) = (a [b,c])
1. anticommutativity: [a,b] = -[b,a]
2. distributive property: [a,(b+c)] = [a,b] + [a,c]
3. associativity: [(f a),b] = [a,(f b)] = f [a,b]
4. vector triple product: [a,[b,c]] = b(ac) - c(ab)
5. [a,a] = 0
6. [[a,b],c] + [[b,c],a] + [[c,a],b] =0
7. mixed triple product: ([a,b] c) = (a [b,c])
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