Math Problem Statement

Прямую в пространстве можно зафиксировать, задав:

Solution

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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Math Problem Analysis

Mathematical Concepts

Linear Geometry
3D Space
Vector Mathematics

Formulas

Equation of a line: r(t) = r0 + tv
Parametric equation for a line: (x - x0)/a = (y - y0)/b = (z - z0)/c

Theorems

Line Uniqueness in 3D Space

Suitable Grade Level

Grades 10-12