Force equilibrium vector triangle for ladder

Steps:

• Identify forces: weight W acts vertically downward at center G; P is total reaction at rough ground (upward normal + horizontal friction toward wall); Q is total reaction at rough wall (horizontal normal away from wall + vertical friction upward).
• For translational equilibrium, vector sum P + Q + W = 0, forming a closed triangle where vectors connect head-to-tail.
• Sketch triangle: start with W downward; P must oppose by pointing upward and toward wall; Q closes by pointing leftward and upward.
• Verify directions: friction ensures no slipping, so P inclines up-right, Q up-left, balancing W vertically.

Why A is correct:

• A depicts closed triangle with W vertical down, P up-right, Q up-left, satisfying Lami's theorem for equilibrium directions.

Why the others are wrong:

• B shows W not vertical, violating gravity direction.
• C has P vertical only, ignoring ground friction.
• D positions Q downward, contradicting wall friction opposing slip.

Final answer: A