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

Here’s a breakdown of the exercise:

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**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.

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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!

Représenter les directions des rangées : [010], [110], [120], [101] et déterminer la rangée [uvw] qui passe par les couples de nœuds suivants: 432 et 120, 321 et 131, 001 et 101.

This exercise covers key concepts in crystallography, including how to represent crystallographic directions such as [010], [110], [120], and [101]. It also involves calculating the [uvw] direction passing through pairs of nodes in a crystal lattice.

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