Systems of Forces — Classification Forces that do not meet at a single point and whose lines of action do not lie in the same plane are classified as which type of system?

Introduction / Context: Classifying force systems is a first step in solving equilibrium and resultant problems. Two attributes matter: whether the lines of action lie in one plane (coplanarity) and whether they intersect at a point (concurrency).

Given Data / Assumptions:

• Lines of action: not in the same plane (non-coplanar).
• Forces do not meet at a single point (non-concurrent).

Concept / Approach: Possible standard categories include coplanar concurrent, coplanar non-concurrent, and non-coplanar concurrent. The described case is both non-coplanar and non-concurrent, which is not listed among the options; hence “None of these” is appropriate.

Step-by-Step Reasoning:

Verification / Alternative check: In 3D statics, the most general force system is non-coplanar and non-concurrent, requiring six equilibrium equations for a rigid body (three force and three moment components).

Why Other Options Are Wrong: Options (a) and (b) require coplanarity; option (c) requires concurrency — all contradict the problem statement.

Common Pitfalls: Overlooking that 3D systems cannot be simplified with 2D (coplanar) methods; forgetting the extra moment equations needed in 3D equilibrium.

Final Answer: None of these (the correct class is non-coplanar, non-concurrent forces).