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nikcs123

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**cross product "associative triples"**

## Homework Statement

We know that the cross product is not associative, i.e., the identity

(1) [tex](\vec{a}\times\vec{b})\times\vec{c}[/tex] = [tex]\vec{a}\times(\vec{b}\times\vec{c})[/tex] is not true in general. However, certain special triples [tex]\vec{a}[/tex];[tex]\vec{b}[/tex];[tex]\vec{c}[/tex]

of vectors do satisfy (1). For example, if one of the vectors is the zero vector, then (1)

holds trivially, but there are also less obvious examples. Call a triple [tex]\vec{a}[/tex];[tex]\vec{b}[/tex];[tex]\vec{c}[/tex] for which (1)

holds "associative". Characterize all nonzero associative triples by some simple geometric

condition. (An example of a possible condition (though not the correct one) would be that

the three vectors are pairwise perpendicular.)

## The Attempt at a Solution

I attempted to use the properties/identities of cross products to deduce a relationship between the components of each vector and try to piece it together that way, ended up with a huge mess and no progress... Just need a nudge in the right direction on this one.

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