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If (a×b)×c = a×(b×c) where a, b and c are any three vectors such that a·b ≠ 0, b·c ≠ 0 then a and c are

1. inclined at an angle of π/3 between them
2. inclined at an angle of π/6 between them
3. perpendicular
4. parallel

Correct answer: parallel

Solution

(a x b) x c = (a.c)b - (b.c)a and a x (b x c) = (a.c)b - (a.b)c. Equality gives (b.c)a = (a.b)c; since a.b != 0 and b.c != 0, a and c must be parallel.

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