A) \[-2\hat{i}+2\hat{k}\]
B) \[-2\hat{i}-\hat{j}+\hat{k}\]
C) \[2\hat{i}-\hat{j}-2\hat{k}\]
D) \[-\hat{i}+\hat{j}+\hat{k}\]
Correct Answer: B
Solution :
The position vector of centre of mass \[\vec{r}=\vec{r}=\frac{{{m}_{1}}{{{\vec{r}}}_{1}}+{{m}_{2}}{{{\vec{r}}}_{2}}}{{{m}_{1}}+{{m}_{2}}}\] \[=\frac{1(\hat{i}+2\hat{j}+\hat{k})+3(-3\hat{j}-2\hat{j}-\hat{k})}{1+3}\] \[=\frac{1}{4}(-8\hat{i}-4\hat{j}+4\hat{k})\] \[=-2\hat{i}-\hat{j}+\hat{k}\]
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