Definition check — non-coplanar concurrent forces Forces that meet at one point but whose lines of action do not lie in the same plane are called non-coplanar concurrent forces. Choose the correct word to complete the definition.

Introduction / Context:Classifying force systems (coplanar/non-coplanar and concurrent/non-concurrent) is foundational in statics. It dictates which equilibrium equations are needed and whether moments must be considered about axes in 3D.

Given Data / Assumptions:

• Forces intersect at a common point (concurrent).
• Question distinguishes whether the lines of action are in one plane.

Concept / Approach:“Coplanar” means existing in the same geometric plane; “non-coplanar” means spatially distributed in 3D. When forces meet at a point but extend in multiple planes, they are concurrent yet non-coplanar. Hence the missing phrase is “do not lie” in the same plane.

Step-by-Step Solution:Identify concurrency: lines meet at one point.Identify planarity: lines of action are not confined to a single plane.Therefore use the phrase “do not lie”.Select option (b).

Verification / Alternative check:Equilibrium of non-coplanar concurrent forces requires ΣF_x = 0, ΣF_y = 0, and ΣF_z = 0 (three component equations). This directly reflects the 3D nature of non-coplanar systems.

Why Other Options Are Wrong:

• “Lie” would imply coplanar concurrent forces, a different category.

Common Pitfalls:

• Assuming “concurrent” automatically means “coplanar.” They are independent descriptors.

Final Answer:do not lie