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The angle between two vectors of magnitude 12 and 18 units when their resultant is 24 units, is

1. 63°55′
2. 75°52′
3. 82°31′
4. 89°16′

Correct answer: 75°52′

Solution

The magnitude of the resultant vector is given by the formula: R = √(A² + B² + 2ABcosθ). Substituting R = 24, A = 12, and B = 18, we solve for cosθ. This gives cosθ = 0.258, and θ ≈ 75°52′.

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