A body subjected to three concurrent force is found to be in equilibrium. The resultant of any two force

Options

A. is equal to third force
B. is equal to third force
C. is collinear fifth the third force
D. all of these

Explanation

To solve the problem, we need to analyze the conditions for equilibrium of a body subjected to three concurrent forces.

### Step-by-Step Solution:

1. **Understanding Concurrent Forces**:
- Concurrent forces are forces that act at the same point. In this case, we have three forces \( F_1 \), \( F_2 \), and \( F_3 \) acting at a single point.

**Hint**: Remember that concurrent forces meet at a common point.

2. **Condition for Equilibrium**:
- For a body to be in equilibrium under the action of concurrent forces, the vector sum of all forces acting on the body must be zero. This can be expressed mathematically as:
\[ F_1 + F_2 + F_3 = 0 \]
- This implies that one force must be equal in magnitude and opposite in direction to the vector sum of the other two forces.

**Hint**: Think of equilibrium as a balance of forces where the total force equals zero.

3. **Resultant of Two Forces**:
- If we take the resultant of any two forces, say \( F_2 \) and \( F_3 \), it must be equal in magnitude and opposite in direction to the third force \( F_1 \). This can be expressed as:
\[ R_{23} = F_2 + F_3 = -F_1 \]
- This means that the resultant of \( F_2 \) and \( F_3 \) must be equal to \( F_1 \) but in the opposite direction.

**Hint**: Consider how the forces interact; the resultant force must balance the third force.

4. **Collinearity of Forces**:
- Since \( R_{23} \) (the resultant of \( F_2 \) and \( F_3 \)) is equal to \( -F_1 \), it implies that these forces are collinear. This means that all three forces lie along the same line.

**Hint**: Visualize the forces on a straight line to understand their relationships.

5. **Conclusion**:
- Based on the analysis, we can conclude that:
- The resultant of any two forces is equal to the third force.
- The resultant of any two forces is collinear with the third force.
- Therefore, all the statements provided in the question are correct.

**Final Answer**: The correct option is (d) all of these.