Force equilibrium at point X via vector triangle

Steps:

• Identify forces at X: downward weight W, horizontal compressive force Fb from beam toward Y, and tension Fc from cable at an upward angle toward Z.
• For static equilibrium, vector sum of forces must be zero, forming a closed triangle where W + Fb + Fc = 0.
• In the triangle, W is vertical down, Fb horizontal left, Fc diagonal up-right to balance.
• Match triangle sides to force directions and magnitudes per Lami's theorem or parallelogram law.

Why A is correct:

• Option A shows W vertical, Fb horizontal, and Fc diagonal, closing the triangle per force equilibrium law.

Why the others are wrong:

• B: Incorrectly aligns Fc horizontally, violating cable's inclined direction.
• C: Places W horizontally, ignoring gravity's vertical pull.
• D: Reverses Fb direction, implying tension instead of beam compression.

Final answer: A