Consider a vector R in x-y plane as shown in fig.  If we draw orthogonal vectors  R_x and R_y  along x and axes respectively, by law of vector addition,

      where

          and    

Since R and q are usually known, Equation (ii) and (iii) give the magnitude of the components of R along x and y-axes respectively.

Here it is worthy to note once a vector is resolved into its components, the components themselves can be used to specify the vector as –

(1) The magnitude of the vector R is obtained by squaring and adding equation (ii) and (iii), i.e.

(2) The direction of the vector  R is obtained by dividing equation (iii) by (ii), i.e.