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The diagram shows a mechanical system with three forces \( F_1 \), \( F_2 \), and \( F_3 \) acting on a central point. Each force has a magnitude and direction relative to the \( x \)- and \( y \)-axes. To solve this type of problem, we typically need to resolve each force into its horizontal and vertical components and apply the conditions of equilibrium.

### Known Data:
1. \( F_1 = 5 \, \text{kN} \)
2. \( F_2 = 4 \, \text{kN} \)
3. \( F_3 = 6 \, \text{kN} \)

The geometry suggests that:
- \( F_1 \) is at an angle to the positive \( x \)-axis.
- \( F_2 \) is acting along a direction likely near the \( y \)-axis.
- \( F_3 \) is acting downward at some angle to the \( x \)-axis.

### Plan of Solution:
1. **Resolve the forces into components**:
   - For each force, break them into \( x \)- and \( y \)-components using trigonometry.
   
2. **Apply equilibrium conditions**:
   - The sum of forces in the \( x \)-direction must be zero.
   - The sum of forces in the \( y \)-direction must be zero.

### Let's start by resolving the forces.

Do you want to proceed with a detailed calculation, or would you like clarification on any part so far? 

Here are some questions related to this type of problem:

1. How can we calculate the angle of each force from the axis?
2. What are the equations for resolving forces into \( x \)- and \( y \)-components?
3. How do we apply the equilibrium conditions for forces?
4. Can you explain how to calculate the magnitude of the resultant force if the system isn't in equilibrium?
5. How does the system change if one of the forces is removed?

**Tip**: Always check if the system is in equilibrium by verifying the balance of forces in all directions.

A system with three forces (F1 = 5 kN, F2 = 4 kN, and F3 = 6 kN) acting at a central point. Determine the equilibrium by resolving the forces into their x- and y-components.

Learn how to resolve a system of three forces (F1 = 5 kN, F2 = 4 kN, and F3 = 6 kN) into their components and apply equilibrium conditions. This problem covers statics concepts, vector resolution, and the application of equilibrium equations. Suitable for students in Grades 11-12 and college-level mechanics.

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