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If a→ and b→ are any two vectors of magnitudes 1 and 2 respectively, and (1−3a→⋅b→)2+|2a→+b→+3(a→×b→)|2=47, then the angle between a→ and b→ is

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a

π/3

b

π−cos−1⁡(1/4)

c

2π3

d

cos−1⁡(1/4)

answer is C.

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Detailed Solution

1+9(a→⋅b→)2−6(a→⋅b→)+4|a→|2+|b→|2+9|a→×b→|2+4a→⋅b→=47 or 1+4+4+36−4cos⁡θ=47 or cos⁡θ=−12 Hence, the angle between a→ and b→ is 2π3.

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If a→ and b→ are any two vectors of magnitudes 1 and 2 respectively, and (1−3a→⋅b→)2+|2a→+b→+3(a→×b→)|2=47, then the angle between a→ and b→ is