Let the three identical spheres, each of mass $M$, be placed at the coordinates $(0,0)$, $(2,0)$, and $(0,2)$ since the mutually perpendicular sides are along the axes and intersect at the origin. The position vectors of the masses are: $\vec{r}_1 = 0\hat{i} + 0\hat{j}$ $\vec{r}_2 = 2\hat{i} + 0\hat{j}$ $\vec{r}_3 = 0\hat{i} + 2\hat{j}$ The position vector of the centre of mass $\vec{R}_{cm}$ is given by: $\vec{R}_{cm} = \frac{m_1\vec{r}_1 + m_2\vec{r}_2 + m_3\vec{r}_3}{m_1 + m_2 + m_3}$ $\vec{R}_{cm} = \frac{M(0\hat{i} + 0\hat{j}) + M(2\hat{i} + 0\hat{j}) + M(0\hat{i} + 2\hat{j})}{M + M + M}$ $\vec{R}_{cm} = \frac{2M\hat{i} + 2M\hat{j}}{3M}$ $\vec{R}_{cm} = \frac{2}{3}(\hat{i}+\hat{j})$