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Q.

If a→,b→ and c→ be four non-zero vectors such that  [a→b→c→]=1,c→=λa→×b→ angle between  a→ and b→ is 2π/3,|a→|=2|b→|=3 and |c→|=13 the angle between a→ and b→ is

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a

π6

b

π4

c

π3

d

π2

answer is B.

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Detailed Solution

c→=λ(a→×b→) or  c→⋅c→=λ(a→×b→)⋅c→⇒ 13=λ Also |c→|2=λ2|a→×b→|2⇒ 13=19a2b2sin2⁡θ=19×2×3sin2⁡θ or  sin2⁡θ=12 or  θ=π4
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If a→,b→ and c→ be four non-zero vectors such that  [a→b→c→]=1,c→=λa→×b→ angle between  a→ and b→ is 2π/3,|a→|=2|b→|=3 and |c→|=13 the angle between a→ and b→ is