`(n - 1)` equal point masses each of mass `m` are placed at the vertices of a angular n-polygon. The vacent vertex has `a` position vector `a` with respect to the centre of the polygon. Find the position vector of centre of mass.

Explanation

To find the position vector of the center of mass of `(n - 1)` equal point masses each of mass `m` placed at the vertices of an angular n-polygon, with the vacant vertex having a position vector `a` with respect to the center of the polygon, we can follow these steps:

### Step-by-Step Solution:

1. **Understanding the System**:
- We have `(n - 1)` point masses, each of mass `m`, placed at the vertices of a regular n-polygon.
- The n-polygon has `n` vertices, and one vertex is vacant. The position vector of this vacant vertex is given as `a`.

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