A) \[2\hat{i}\,-\hat{j}\,\,-2\hat{k}\]
B) \[-2\hat{i}\,-\hat{j}\,\,+\,\,\hat{k}\]
C) \[-\hat{i}\,+\hat{j}\,\,+\,\,\hat{k}\]
D) \[-\,2\hat{i}\,+2\,\,\hat{k}\]
Correct Answer: B
Solution :
\[{{r}_{cm}}=\frac{{{m}_{1}}{{r}_{1}}+{{m}_{2}}{{r}_{2}}}{{{m}_{1}}+{{m}_{2}}}\] Here, \[{{m}_{1}}\,\,=\,\,1\,\,\,kg;\,\,{{r}_{1}}\,\,=\,\,\hat{i}+2\hat{j}+\hat{k}\] \[{{m}_{2}} = 3 kg;\, {{r}_{2}} = -3\,\hat{i} - 2\,\hat{j} + \hat{k}\] \[\Rightarrow \,\,\,\,\,{{r}_{cm}}=\frac{(1\hat{i}+2\hat{j}+1\hat{k})\times 1+\left( -\,3\hat{i}-2\hat{j}+\hat{k} \right)\times 3}{1+3}\]\[=\,\,\,\,\frac{-\,8\hat{i}-4\hat{j}+4\hat{k}}{4}~\,\,=\,\,-2\,\hat{i}-\hat{j}+\hat{k}\]
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