The image contains an exercise in crystallography, asking about crystallographic directions and planes.

Here’s a breakdown of the exercise:

Exercise n°1: (Crystallographic Directions)

We are working with an orthogonal coordinate system labeled $\vec{a}$, $\vec{b}$, and $\vec{c}$ as shown in the diagram.

1) Represent the directions of the following crystallographic directions:

• $[010]$, $[110]$, $[120]$, $[101]$

For each of these, you will need to express them in terms of the basis vectors $\vec{a}$, $\vec{b}$, and $\vec{c}$ and show how they lie in the coordinate system.

2) Determine the [uvw] direction passing through the following pairs of nodes:

• $432$ and $120$
• $321$ and $131$
• $001$ and $101$

This requires calculating the direction vectors for each pair of points by finding the differences between the coordinates in the crystal lattice.

Would you like a step-by-step solution for part 1 or part 2? Let me know if you'd like to focus on any specific section!