Two bodies of mass 1kg and 3kg have position vectors ^ i + 2 ^ j +...

As we know, centre of mass is given by, $\overset{\to}{r}com = \dfrac{∑ {m}_{i}\overset{\to}{r}i}{∑ {m}_{i}}$

\overset{\to}{r}com = \dfrac{m\left(\overset{^}{ı} + 2\overset{^}{ȷ} + \overset{^}{k}\right) + 3m\left(- 3\overset{^}{ı} - 2\overset{^}{ȷ} + \overset{^}{k}\right)}{m + 3m}

\overset{\to}{r}com = \dfrac{- 8m\overset{^}{ı} - 4m\overset{^}{ȷ} + 4m\overset{^}{k}}{4m} = - 2\overset{^}{ı} - \overset{^}{ȷ} + \overset{^}{k}

The magnitude of the position vector of the centre of mass is $\sqrt{{2}^{2} + {1}^{1} + {1}^{2}} = \sqrt{6}$.

It is similar to the magnitude of the option A.