Given the position vector r = x ex + y ey + z e_z with magnitude r = sqrt(x² + y² + z²).

Here are the solutions to the exercises:

EXERCICE 1:
Given the position vector $\vec{r} = x \vec{e_x} + y \vec{e_y} + z \vec{e_z}$ with magnitude $r = \sqrt{x^2 + y^2 + z^2}$.

Step 1: Calculate $\text{grad } r$
The gradient of a scalar function $f(x, y, z)$ is given by $\vec{\nabla} f = \frac{\partial f}{\partial x} \vec{e_x} + \frac{\partial f}{\partial y} \vec{e_y} + \frac{\partial f}{\partial z}