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GATE2018-2-28

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For a position vector $\overrightarrow{r} = x \hat{i}+y \hat{j} + z\hat{k}$ the norm of the vector can be defined as $\mid \overrightarrow{r} \mid = \sqrt{x^2+y^2+z^2}$. Given a function $\phi =\text{ln} \mid \overrightarrow{r} \mid$, its gradient $\nabla \phi$ is

  1. $\overrightarrow{r}\\ $
  2. $\dfrac{\overrightarrow{r}}{\mid \overrightarrow{r} \mid}  \\ $
  3. $\dfrac{\overrightarrow{r}}{\overrightarrow{r} \cdot \overrightarrow{r} }  \\ $
  4. $\dfrac{\overrightarrow{r}}{\mid \overrightarrow{r} \mid^3} $
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