If |A × B| = √3A . B, then the value of |A + B| is

(A² + B² + √3AB)½
(A² + B² + AB)½
(A² + B² + AB/√3)½
A + B

Correct answer: (A² + B² + √3AB)½

Solution

The given condition |A × B| = √3A . B implies that the angle between vectors A and B is 60°. Using the formula for the magnitude of the resultant vector |A + B| = √(A² + B² + 2ABcosθ), substituting θ = 60° and cos60° = 1/2, we get |A + B| = √(A² + B² + AB√3).

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