Rectangular Cartesian Components | Force Projections

**Application of Unit
Vector:** In an alternative representation, the force of
magnitude F is acting in the direction of line AB with coordinates
of A and B clearly defined.

In this case, we can represent in terms of its magnitude and the unit vector in the same direction

where is the unit vector in the direction of . In this formulation, the magnitude and the direction of the force vector are identified separately whereas in the Cartesian formulation they are combined together.

**Position Vector:** For calculation of the
unit vector we make use of the position vector. We determine the
position vector by subtracting the coordinates of its tail from
those of its head as follows.

Knowing the position vector and its magnitude, we find the unit vector as

Notice that the angle q, used previously to describe the direction of , can be determined as