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Точки M и N – середины ребер CC1 и BC параллелепипеда  ABCDA1B1C1D1. Укажите верное утверждение.



Выберите один ответ:
BC1→
 ↑↑
 CB1→
 

NM→
 ↑↓
 BC1→
 

BC→
 = A1D1→
 

MN→
 = AD1→
 


Looking at the diagram of the parallelepiped \( ABCDA_1B_1C_1D_1 \), the points \( M \) and \( N \) are midpoints of edges \( CC_1 \) and \( BC \) respectively.

Now, let's analyze the given statements:

1. **\( \vec{BC_1} \parallel \vec{CB_1} \)**:
   - This is **true** because the vector from \( B \) to \( C_1 \) and the vector from \( C \) to \( B_1 \) are parallel due to the geometric symmetry of the parallelepiped. These vectors represent opposite edges of the same plane.

2. **\( \vec{NM} \parallel \vec{BC_1} \)**:
   - This is **false**. The vector \( \vec{NM} \) (from \( N \) to \( M \)) does not point in the same direction as the vector from \( B \) to \( C_1 \).

3. **\( \vec{BC} = \vec{A_1D_1} \)**:
   - This is **false** because \( \vec{BC} \) and \( \vec{A_1D_1} \) are not equal. They are parallel but do not have the same magnitude and direction.

4. **\( \vec{MN} = \vec{AD_1} \)**:
   - This is **true**. Since \( M \) and \( N \) are midpoints and due to the symmetry of the parallelepiped, \( \vec{MN} \) is parallel and equal in length to \( \vec{AD_1} \).

The **correct answer** is:  
- **\( \vec{MN} = \vec{AD_1} \)**.

Would you like a further breakdown or more details on any of these statements?

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Here are some related questions:

1. What is the geometric significance of a parallelepiped?
2. How do midpoints of edges in a parallelepiped affect the vector relations?
3. Can two vectors of different magnitude still be parallel?
4. How would you find the length of a vector in a parallelepiped?
5. What other properties of vectors can be inferred from the symmetry of a parallelepiped?

**Tip:** When working with vectors in 3D shapes, symmetry and parallelism often simplify complex relationships.

Точки M и N – середины ребер CC1 и BC параллелепипеда ABCDA1B1C1D1. Укажите верное утверждение.

Solve a geometry problem involving a parallelepiped ABCDA1B1C1D1, where points M and N are the midpoints of edges CC1 and BC. Learn how to determine vector relationships and correct parallelism within this 3D shape.

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