In a rectangular coordinate system, the equilibrium equations can be represented by three scalar equations. What is this form called?

In a rectangular coordinate system, the equilibrium equations can be represented by three scalar equations. What is this form called?

• A. Equilibrium equation in component form
• B. Free body diagram
• C. String or Cable
• D. Linear Spring

Answer: (A)

Balancing forces along each axis after breaking all forces into their x, y, and z components gives three independent scalar equations: the sums of the x-components, y-components, and z-components must each be zero. This is the equilibrium equations expressed in component form, because it converts the vector condition ΣF = 0 into separate equations along the coordinate directions. The other options are not forms of the balance equations: a free body diagram is just a visualization tool for forces, while a string or cable and a linear spring are physical elements that transmit force or relate force to displacement, not the statement of equilibrium itself.

Balancing forces along each axis after breaking all forces into their x, y, and z components gives three independent scalar equations: the sums of the x-components, y-components, and z-components must each be zero. This is the equilibrium equations expressed in component form, because it converts the vector condition ΣF = 0 into separate equations along the coordinate directions. The other options are not forms of the balance equations: a free body diagram is just a visualization tool for forces, while a string or cable and a linear spring are physical elements that transmit force or relate force to displacement, not the statement of equilibrium itself.