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Let a, b and c be three unit vectors such that a×(b×c) = (√3/2)(b + c). If b is not parallel to c, then the angle between a and b is:

1. 2π/3
2. 5π/6
3. 3π/4
4. π/2

Correct answer: 5π/6

Solution

Expanding, a x (b x c) = (a.c)b - (a.b)c = (sqrt(3)/2)(b + c). Since b is not parallel to c, compare coefficients: a.c = sqrt(3)/2 and -(a.b) = sqrt(3)/2, so a.b = -sqrt(3)/2. With unit vectors, cos(theta) = -sqrt(3)/2, giving theta = 5*pi/6.

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