Fig. 3-3 Resolution of a force into components

Any force can be resolved into the addition of two mutually perpendicular forces which are called components of force. The components of force are resolved along the x-axis and the y-axis of a given coordinate system. From Fig. 3-3, we see that

x-component:
y-component:

In fact, the resultant force of a system can be found by resolving all the forces into their x and y-components, and then adding up the components in each direction. The following animation illustrates the tip-to-tail method of adding vectors, as well as the method of resolving components.

Flash animation: The addition of forces

 Fig. 3-4 A car at rest downhill.

Consider a car at rest downhill as shown in Fig. 3-4. The road exerts a reaction force on the car, in a direction normal to the road. There friction acting on the tyres of the car, preventing it from sliding downhill. The weight of the car can be resolved into components, namely, along the road (along x-axis) and perpendicular to the road (along y-axis). The components along each axis can be added together algebraically to give the resultant force. Since the car is at rest, the resultant force is zero, and the components along each axis must be balanced:

x-component (parallel to the road):

y-component (normal to the road):