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A and B are two vectors and θ is the angle between them. If |A × B| = √3(A.B), the value of θ is

1. 45°
2. 30°
3. 90°
4. 60°

Correct answer: 60°

Solution

The magnitude of the cross product is |A × B| = |A||B|sinθ, and the dot product is A.B = |A||B|cosθ. Given |A × B| = √3(A.B), substituting these gives |A||B|sinθ = √3|A||B|cosθ. Dividing through by |A||B| (non-zero), we get tanθ = √3, which implies θ = 60°.

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