Question
Show that there is one and only one set of resolved components in a particular direction.
Solution
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 
.
That is, 
Since, 
are components of 
,
Therefore, 
And also, 
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.
