The unit vector perpendicular to both $\hat{i}+\hat{j}$ and $\hat{j}-\hat{k}$ is

Q. The unit vector which, is perpendicular to the vectors $\overrightarrow{A}=\hat{i}-2\hat{j}+\hat{k}$ and $\overrightarrow{B}=3\hat{i}-2\hat{j}-\hat{k}$ is

Q. If $\overrightarrow{r}.\hat{i}=\overrightarrow{r}.\hat{j}=\overrightarrow{r}.\hat{k}$ and $|r|=3$, then find $\overrightarrow{r}$.

Q. If $\overrightarrow{r}.\hat{i}=\overrightarrow{r}.\hat{j}=\overrightarrow{r}.\hat{k}\text{and}|\overrightarrow{r}|=3,\text{then}\overrightarrow{r}$ is equal to

Q. With respect to a rectangular cartesian co-ordinate system three vectors are expressed as $\overrightarrow{a}=4\hat{i}-\hat{j},\overrightarrow{b}=-3\hat{i}+2\hat{j}$ and $\overrightarrow{c}=-\hat{k}$ where $\hat{i},\hat{j}$ and $\hat{k}$ are unit vectors along the x, y, z axes respectively. The unit vector along the direction of sum of these vectors is

Q.

With respect to a rectangular cartesian coordinate system, three vectors are expressed as $\overrightarrow{a}=4\hat{i}-\hat{j},\overrightarrow{b}=-3\hat{i}+2\hat{j}$ and
$\overrightarrow{c}=-\hat{k}$ 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