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consider,
∑ vector (a x ( b x c)) = vector (a x ( b x c) + vector (b x ( c x a)) + vector (c x ( a x b))
= vector {( c • a ) b) – ( b • a ) c} + vector {(b • a) c) – (b • c) a} + vector {(c • b )a) – ( c • a) b}
= 0
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