Example 1: Express each force vector in terms of its Cartesian components and determine the resultant force vector.

Each force vector can be represented in terms of its two vectors components along x, y axes

The resultant force can also be expressed in terms of its x, y vector components as

Since can also be expressed as

We arrive at

Realizing that each vector can be represented by the product of its magnitude and the unit vector in the same direction, we can write

Where

Now, we can express the resultant force vector in terms of its Cartesian components as

or simply

The magnitude of the resultant force vector is obtained as

and its direction can be measured from the x axis as