With respect to a rectangular cartesian coordinate system, three vectors are expressed as \( \ve...

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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 vector \( \hat{r} \) 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) \( \hat{r}=\frac{1}{\sqrt{2}}(\hat{i}+\hat{j}+\hat{k}) \)
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