Ans.

Position vector of A is \( (-\hat{i}-2\hat{j}+2\hat{k}) \)

Position vector of B is \( (3\hat{i}+2\hat{j}-\hat{k}) \)

Position vector of C is \( (\hat{i}-2\hat{j}+4\hat{k}) \) and

Position vector of D is \( (3\hat{i}+\hat{j}+2\hat{k}) \).

So the centre of mass of the system is given by,

\( \vec{R}=\frac{(-\hat{i}-2\hat{j}+2\hat{k})+2(3\hat{i}+2\hat{j}-\hat{k})+3(\hat{i}-2\hat{j}+4\hat{k})+4(3\hat{i}+\hat{j}+2\hat{k})}{1+2+3+4} \)

or, \( \vec{R}=\frac{(20\cdot\hat{i}+0\cdot\hat{j}+20\cdot\hat{k})}{10} \)

or, \( \vec{R}=(2\hat{i}+0\hat{j}+2\hat{k}) \)

So the co-ordinate of the centre of mass of the system is (2,0,2)