Let a given vector be resolved in the direction of two non-parallel vectors .
Let there be two sets of resolved components of resultant in the direction of .
Since, are components of ,
So, from equations (1) and (2), we have,
Since, vector A and B are different non-parallel vectors, so equation (3) is possible only and only if,
Hence, both the sets of components are identical. There is one and only one set of resolved components in a particular direction.