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# Three particles, each of mass m are placed at the vertices of a right angled triangle as shown in figure. The position vector of the centre of mass of the system is ( O is the origin and $\overrightarrow i , \overrightarrow j, \overrightarrow k$ are unit vectors )

$\begin {array} {1 1} (1)\;\large\frac{1}{3}( a\overrightarrow i - b \overrightarrow j) & \quad (2)\;\large\frac{2}{3} ( a \overrightarrow i + b \overrightarrow j) \\ (3)\;\large\frac{2}{3} ( a \overrightarrow i - b \overrightarrow j) & \quad (4)\;\large\frac{1}{3} ( a \overrightarrow i + b \overrightarrow j) \end {array}$

(4) $\large\frac{1}{3} (a \overrightarrow i + b \overrightarrow j)$