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The question in the image asks how a line in space can be uniquely determined. The options are in Russian, and they translate to:

1. A point on the line and a guiding vector.
2. Two points on the line.
3. A point on the line and the plane containing the line.
4. A point on the line and a normal vector to it.

The correct answer is **Option 1: A point on the line and a guiding vector** or **Option 2: Two points on the line**. Both methods will fully determine a line in three-dimensional space.

Would you like further explanation of these concepts, or do you have any questions?

Here are 5 related questions:
1. How do you represent a line in 3D space using parametric equations?
2. What is the difference between a guiding vector and a normal vector?
3. How can you describe the intersection of two planes?
4. How would you calculate the angle between two lines in space?
5. What is the role of the cross product in determining the direction of a line?

**Tip**: Always ensure that both the point and the vector (or two points) used to define a line are not collinear with the plane you're describing for uniqueness.

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Explore how to uniquely determine a line in 3D space by using two points or a point with a guiding vector. Understand key concepts in linear geometry and vector mathematics, including the parametric equation of a line. Suitable for high school students in Grades 10-12.

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