﻿ Show that there is one and only one set of resolved components in a particular direction. from Physics Motion in A Plane Class 11 Manipur Board

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Show that there is one and only one set of resolved components in a particular direction.

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.

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