Two forces, 3 N due North and 4 N due East, act on an object. Calculate the resultant force and the equilibrium force.

The first force $F_1$ is $3 \, \text{N}$ acting Due North.
The second force $F_2$ is $4 \, \text{N}$ acting Due East.
Since North and East are perpendicular directions, the angle between the two forces is $90^\circ$.

The magnitude of the resultant force $R$ of two perpendicular forces can be found using the Pythagorean theorem:

Let $\theta$ be the angle the resultant force makes with the East direction.

So, the resultant force is $5 \, \text{N}$ at an angle of approximately $36.87^\circ$ North of East.

The equilibrium force is a single force that, when added to the original forces, results in a net force of zero. Therefore, the equilibrium force has the same magnitude as the resultant force but acts in the exact opposite direction.
Magnitude of equilibrium force:

Direction of equilibrium force:
Since the resultant force is $36.87^\circ$ North of East, the equilibrium force will be $36.87^\circ$ South of West.

The equilibrium force is $\text{5 N at } 36.87^\circ \text{ South of West}$.