Unit Vectors

A vector is completely specified by writing down magnitude and direction (i.e. A and θ) x and y components (A_x and A_y). There's another very useful and compact way to write vectors and that is by using unit vectors. The unit vector  is defined to always have a length of 1 and to always lie in the positive x direction, as in Fig. 1.1. (The symbol ^ is used to denote these unit vectors.)

FIGURE 1.1  Unit vector .

Similarly the unit vector  is defined to always have a length of 1 also but to lie entirely in the positive y direction.

FIGURE 1.2 Unit vector  .

The unit vector  lies in the psoitive z direction.

FIGURE 1.3 Unit vector .

Thus any arbitrary vector  is now written as

(Think about this and make sure you understand.)