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.

Given data
Two fixed magnitudes P and Q with included angle θ.

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

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

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

Final Answer
0° and 180°