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SSC Applied Mathematics QUESTION #4139
Question 1
What is $\nabla \times \vec{r}$ where $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$?
  • $\vec{r}$
  • $\vec{0}$✔️
  • $3\hat{k}$
  • $\frac{\vec{r}}{r}$
Correct Answer Explanation
$\nabla \times \vec{r} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \ \partial_x & \partial_y & \partial_z \ x & y & z \end{vmatrix} = \hat{i}(0-0) - \hat{j}(0-0) + \hat{k}(0-0) = \vec{0}$.