A) \[\hat{r}=\frac{1}{\sqrt{3}}(\hat{i}+\hat{j}-\hat{k})\]
B) \[\hat{r}=\frac{1}{\sqrt{2}}(\hat{i}+\hat{j}-\hat{k})\]
C) \[\hat{r}=\frac{1}{3}(\hat{i}-\hat{j}+\hat{k})\]
D) \[\hat{r}=\frac{1}{\sqrt{2}}(\hat{i}+\hat{j}+\hat{k})\]
Correct Answer: A
Solution :
\[\vec{r}=\vec{a}+\vec{b}+\vec{c}\]\[=4\hat{i}-\hat{j}-3\hat{i}+2\hat{j}-\hat{k}\]\[=\hat{i}+\hat{j}-\hat{k}\] \[\hat{r}=\frac{{\vec{r}}}{|r|}=\frac{\hat{i}+\hat{j}-\hat{k}}{\sqrt{{{1}^{2}}+{{1}^{2}}+{{(-1)}^{2}}}}=\frac{\hat{i}+\hat{j}-\hat{k}}{\sqrt{3}}\]
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