For a position vector \[{\rm{r}} = {\rm{x\hat i}} + {\rm{y\hat j}} + {\rm{z\hat k}}\] the norm of the vector can be defined as $$\left| {\overrightarrow {\text{r}} } \right| = \sqrt {{{\text{x}}^2} + {{\text{y}}^2} + {{\text{z}}^2}} .$$ Given a function $$\phi = \ln \left| {\overrightarrow {\text{r}} } \right|,$$ its gradient $$\nabla \phi $$ is A. $$\overrightarrow {\text{r}} $$ B. $$\frac{{\overrightarrow {\text{r}} }}{{\left| {\overrightarrow {\text{r}} } \right|}}$$ C. $$\frac{{\overrightarrow {\text{r}} }}{{\overrightarrow {\text{r}} \cdot \overrightarrow {\text{r}} }}$$ D. $$\frac{{\overrightarrow {\text{r}} }}{{{{\left| {\overrightarrow {\text{r}} } \right|}^3}}}$$

The correct answer is $\boxed{\frac{{\overrightarrow {\text{r}} }}{{\left| {\overrightarrow {\text{r}} } \right|}}}$.

The gradient of a scalar field $\phi$ is a vector field that points in the direction of the greatest rate of increase of $\phi$, and its magnitude is equal to the magnitude of the rate of increase of $\phi$. In other words, the gradient of $\phi$ is the vector field that tells you how fast $\phi$ is changing at each point in space.

In this case, the scalar field is $\phi = \ln \left| {\overrightarrow {\text{r}} } \right|$, which is the natural logarithm of the magnitude of the position vector. The rate of change of $\phi$ in the direction of $\overrightarrow {\text{r}}$ is $\frac{\partial \phi}{\partial \overrightarrow {\text{r}}} = \frac{\overrightarrow {\text{r}} }{{\left| {\overrightarrow {\text{r}} } \right|}}$. Therefore, the gradient of $\phi$ is $\nabla \phi = \frac{{\overrightarrow {\text{r}} }}{{\left| {\overrightarrow {\text{r}} } \right|}}$.

The other options are incorrect because they do not point in the direction of the greatest rate of increase of $\phi$. For example, $\overrightarrow {\text{r}}$ does not point in the direction of the greatest rate of increase of $\phi$ because it is not always in the same direction as the gradient of $\phi$.