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Let a, b and c be non-zero vectors such that (a × b) × c = 1/3 |b| |c| a. If q is the acute angle between the vectors b and c, then sin q equals

1. 2√2 / 3
2. √2 / 3
3. 2 / 3
4. 1 / 3

Correct answer: 2√2 / 3

Solution

Using (a x b) x c = (a.c)b - (b.c)a = (1/3)|b||c|a gives a.c=0 and b.c = -(1/3)|b||c|. For the acute angle q, cos q = 1/3, so sin q = sqrt(1 - 1/9) = 2sqrt(2)/3.

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