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Question:

If vectors a and b are such that |a|=3, |b|=2√3 and a x b is a unit vector, then write the angle between a and b.

Solution:

Here, |a|=3 and |b|=2√3 and |a x b|=1
We know that a x b = |a|.|b|sinθ
⇒1 = 3.2√3.sinθ
1 = 6√3 sinθ
sinθ = 1/(6√3)
θ = π/6