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Let's analyze the given statements one by one:

1. **"Скалярное произведение нормальных векторов плоскостей, принадлежащих одной связке плоскостей, всегда отлично от нуля."**
   - This statement is **incorrect**. If two planes belong to the same "family" of planes, their normal vectors might be parallel. In such a case, their scalar product could be zero.

2. **"Плоскость \(2x + 4y - z + 8 = 0\) пересекает ось \(Ox\) в точке \((-4; 0; 0)\)."**
   - To find the intersection of this plane with the \(Ox\) axis, set \(y = 0\) and \(z = 0\) and solve for \(x\):
     \[
     2x + 8 = 0 \quad \Rightarrow \quad x = -4.
     \]
     Thus, the point of intersection is \((-4, 0, 0)\), making this statement **correct**.

3. **"Плоскость \(2y - 1 = 0\) параллельна координатной плоскости \(XOZ\)."**
   - The equation of the plane simplifies to \(y = \frac{1}{2}\), which is a plane parallel to the \(XOZ\) plane (since it only shifts along the \(y\)-axis). Hence, this statement is **correct**.

4. **"Уравнения \(2x + y - z + 1 = 0\) и \(2x + y + z - 1 = 0\) определяют одну и ту же плоскость."**
   - To determine if these two equations represent the same plane, subtract the second equation from the first:
     \[
     (2x + y - z + 1) - (2x + y + z - 1) = 0,
     \]
     which simplifies to:
     \[
     -2z + 2 = 0 \quad \Rightarrow \quad z = 1.
     \]
     Since this leads to \(z = 1\), it shows that the two equations represent different planes. Therefore, this statement is **incorrect**.

### Summary of Correct Statements:
- The second statement about the plane intersecting the \(Ox\) axis at \((-4, 0, 0)\).
- The third statement about the plane \(2y - 1 = 0\) being parallel to the \(XOZ\) plane.

Would you like more details or have any further questions?

Here are 5 related questions:
1. How can you determine if two planes are parallel?
2. What does the scalar product of two normal vectors represent geometrically?
3. How do you find the intersection of a plane with a specific axis?
4. What is the relationship between the equations of two parallel planes?
5. How can we verify if two planes are identical based on their equations?

**Tip:** When checking if two planes are parallel, their normal vectors should be scalar multiples of each other.

Укажите все верные утверждения: Скaлярное произведение нормальных векторов плоскостей... [user's screenshot text continues].

Рассматриваем утверждения о пересечении и параллельности плоскостей, а также свойства скалярного произведения нормальных векторов. Подходит для учеников 10-11 классов.

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