Two forces A and B act at a point. If their resultant is [given by] (B - A) in the direction of B, then

Analyze the question: Two forces A and B act at a point. Their resultant has magnitude (B − A) and points in the direction of B. We need to find what this tells us about the forces.

Concept: The resultant of two forces depends on the angle θ between them:

R² = A² + B² + 2AB cosθ

• θ = 0° (same direction): R = A + B
• θ = 180° (opposite directions): R = |B − A|
• θ = 90°: R = √(A² + B²)

Solution:

1. The resultant is B − A. This is a difference of magnitudes, not a sum. That only happens when the forces act in opposite directions.
2. Check with θ = 180°: cos 180° = −1, so R² = A² + B² − 2AB = (B − A²)... more precisely R² = (B − A)², so R = B − A.
3. The resultant points along B, so B is the larger force (B > A). This matches the requirement that B − A is positive.
4. Check the other options: • A (A = B): the resultant would be zero, so there would be no direction. Wrong. • B (A > B): B − A would be negative and the resultant would point along A. Wrong. • C (0°): the resultant would be A + B. Wrong. • D (90°): the resultant would be √(A² + B²). Wrong. • E (180°): gives B − A along B when B > A. Correct.

Answer: E. The forces act in opposite directions, so the angle between them is 180°.

Tip: Whenever a resultant is the difference of two forces, think "opposite directions, 180°". When it is the sum, think "same direction, 0°". The larger force decides the direction of the resultant.