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

As we know, centre of mass is given by, ${\overrightarrow{r}}_{\mathrm{com}}=\frac{\sum m_i{\overrightarrow{r}}_i}{\sum m_i}$

${\overrightarrow{r}}_{\mathrm{com}}=\frac{m\left(\hat{\mathrm{ı}}+2\hat{\mathrm{ȷ}}+\hat{\mathrm{k}}\right)+3m\left(-3\hat{\mathrm{ı}}-2\hat{\mathrm{ȷ}}+\hat{\mathrm{k}}\right)}{m+3m}$

${\overrightarrow{r}}_{\mathrm{com}}=\frac{-8m\hat{\mathrm{ı}}-4m\hat{\mathrm{ȷ}}+4m\hat{\mathrm{k}}}{4m}=-2\hat{\mathrm{ı}}-\hat{\mathrm{ȷ}}+\hat{\mathrm{k}}$

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.