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Resultant of two forces: angles for extremal magnitude For two forces of fixed magnitudes, the resultant is maximum at which angle between them, and minimum at which angle (respectively)? Choose the correct ordered pair.

Difficulty: Easy

0° and 180°
180° and 0°
90° and 180°
90° and 0°

Correct Answer: 0° and 180°

Explanation:

Given dataTwo fixed magnitudes P and Q with included angle θ.

Concept/ApproachResultant magnitude: R = √(P² + Q² + 2PQ cosθ).

Step-by-stepR is maximum when cosθ = 1 ⇒ θ = 0° (same direction).R is minimum when cosθ = −1 ⇒ θ = 180° (opposite directions).

Common pitfallsThinking 90° gives minimum; at 90°, R = √(P² + Q²), which is intermediate.

Final Answer0° and 180°

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