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The question is asking about the relationship between a vector **a** and its unit vector (орт) denoted as **a₀**. The unit vector **a₀** is derived from vector **a** by dividing the vector by its magnitude, i.e.,

\[
\vec{a₀} = \frac{\vec{a}}{|\vec{a}|}
\]

Let’s analyze the statements one by one:

1. **Они всегда сонаправленны. (They are always in the same direction.)**  
   This is **true**, because the unit vector points in the same direction as the original vector, but it has a magnitude of 1.

2. **Они всегда равны. (They are always equal.)**  
   This is **false**, because the unit vector has a magnitude of 1, while the original vector can have any magnitude.

3. **Они всегда ортогональны. (They are always orthogonal.)**  
   This is **false**, because the unit vector is not orthogonal to the original vector; it is in the same direction.

4. **Они всегда коллинеарны. (They are always collinear.)**  
   This is **true**, because the unit vector is a scaled version of the original vector, which makes them collinear.

### Correct choices:
- Они всегда сонаправленны. (They are always in the same direction.)
- Они всегда коллинеарны. (They are always collinear.)

Would you like further details or explanations?

Here are 5 related questions to deepen your understanding:
1. What is the difference between collinear and coplanar vectors?
2. How is the magnitude of a vector calculated?
3. What is the significance of the dot product in determining the relationship between two vectors?
4. Can two vectors be both collinear and orthogonal? Why or why not?
5. What is the geometric interpretation of a unit vector?

**Tip:** When normalizing a vector, you are essentially scaling it to have a magnitude of 1, but its direction remains unchanged.

Пусть задан вектор a и его орт a₀. Что можно сказать об этих векторах? (Выберите все верные утверждения).

Learn about the relationship between a vector and its unit vector with this detailed explanation. Understand why they are always in the same direction, but not always equal, and explore the concepts of collinearity and orthogonality in vector algebra. Suitable for Grades 9-12.

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