(n – 1) equal point masses each of mass m are placed at the vertices of a regular n-polygon. The vacant vertex has a position vector $\overrightarrow{\mathrm{a}}$ w.r.t the centre of polygon. The position vector of centre of mass is 

Let x represent the mass center's distance.

$(\mathrm{n}-1)\mathrm{mx}+\mathrm{m}\overrightarrow{\mathrm{a}}=0$

$(\mathrm{n}-1)\mathrm{mx}=-\mathrm{m}\overrightarrow{\mathrm{a}}$

$\mathrm{x}=-\frac{\overrightarrow{\mathrm{a}}}{(\mathrm{n}-1)}$

According to the position vector of the unoccupied vertex, the centre of mass will move in the opposite direction.

Hence the correct answer is $-\frac{\overrightarrow{\mathrm{a}}}{(\mathrm{n}-1)}.$