With respect to a rectangular cartesian coordinate system, three vectors are expressed as \[\vec{a}=4\hat{i}-\hat{j}\], \[\vec{b}=-3\hat{i}+2\hat{j}\] and \[\vec{c}=-\hat{k}\] where \[\hat{i},\,\hat{j},\,\hat{k}\]are unit vectors, along the X, Y and Z-axis respectively. The unit vectors \[\hat{r}\]along the direction of sum of these vector is [Kerala CET (Engg.) 2003]

• 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.            \[\hat{r}=\frac{1}{\sqrt{2}}(\hat{i}+\hat{j}+\hat{k})\]