To understand why two force members must be in the opposite direction to be in equilibrium, let's first define what equilibrium means. In mechanics, equilibrium refers to a state in which the net force acting on an object is zero, resulting in no acceleration or movement.

In this context, if two force members are in equilibrium, it means that the combined effect of these forces is zero, and they balance each other out. This condition can only be achieved when the two forces are equal in magnitude and opposite in direction. Let's discuss this further:

1. Equal Magnitude:
- When two forces are of equal magnitude, it means they have the same strength or intensity.
- If the forces have different magnitudes, the stronger force will dominate and cause the object to accelerate in that direction, violating the condition of equilibrium.
- Therefore, for equilibrium, the magnitudes of the two forces must be equal.

2. Opposite Direction:
- For two forces to cancel each other out, they must act in opposite directions.
- When the forces are in the same direction, they would add up, resulting in a net force that is not zero, leading to acceleration or movement.
- However, when the forces are in opposite directions, their magnitudes subtract, and if they are equal, the net force becomes zero.
- Consequently, the object remains in a state of equilibrium.

3. Cancellation of Forces:
- When two forces are equal in magnitude and opposite in direction, they cancel each other out.
- The forces effectively neutralize each other's effects, resulting in no net force acting on the object.
- This cancellation occurs because the forces have the same magnitude but act in opposite directions, creating a balance.

In summary, for two force members to be in equilibrium, they must have equal magnitudes and act in the opposite direction. This ensures that their effects cancel each other out, resulting in a net force of zero. This concept is fundamental in understanding the conditions required for equilibrium in mechanical systems.