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SSC Applied Mathematics QUESTION #4134
Question 1
For $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$ and $r = |\vec{r}|$, what is $\nabla r$?
  • $\vec{r}$
  • $\frac{\vec{r}}{r}$✔️
  • $\frac{\vec{r}}{r^2}$
  • $\hat{r}$
Correct Answer Explanation
$\nabla r = \frac{\partial r}{\partial x}\hat{i} + \frac{\partial r}{\partial y}\hat{j} + \frac{\partial r}{\partial z}\hat{k} = \frac{x}{r}\hat{i} + \frac{y}{r}\hat{j} + \frac{z}{r}\hat{k} = \frac{\vec{r}}{r}$.