# Vectors

###### Sections

##### Components of a vector

Figure 12

Consider a vector with length a, Figure 12. Let the angle it makes with the x-axis be θ. The angle is always measured by starting with the positive x-direction and rotating anti-clockwise until the vector is reached.

The x component of the vector, denoted a_{x}, is given by

(3)

The y component is given by

(4)

These relations hold for any angle θ, even if it is more than 90^{0}.

Convince yourself that these relations hold for the four cases where the vector with its tail at the origin, has its head in each of the four quadrants.