Math Problem Statement

Скільки площин, перпендикулярних даній, можна провести через точку, яка не лежить на площині?

Solution

The question in the image asks:

"Скільки площин, перпендикулярних даній, можна провести через точку, яка не лежить на площині?"

Translation: "How many planes perpendicular to a given plane can pass through a point that does not lie on the plane?"

Answer:

Through a point that does not lie on a given plane, one and only one plane can be drawn perpendicular to the given plane. This is because for a plane to be perpendicular, its normal vector (the line perpendicular to the plane) must pass through the point in question. Since the normal is unique, the perpendicular plane is unique as well.

Would you like more details or have any other questions?

Relative Questions:

  1. What is the definition of a perpendicular plane?
  2. How is a plane uniquely determined in 3D space?
  3. What is the geometric relationship between a point and a plane in 3D geometry?
  4. Can multiple planes pass through the same point but with different orientations?
  5. What are the conditions for two planes to be perpendicular?

Tip:

In 3D geometry, the perpendicularity of planes is determined by their normal vectors—two planes are perpendicular if their normal vectors are perpendicular.

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Math Problem Analysis

Mathematical Concepts

Geometry
3D Planes
Perpendicular Planes

Formulas

None directly, but involves understanding of vectors and planes in 3D space

Theorems

Uniqueness of perpendicular planes through a point in 3D space

Suitable Grade Level

Grades 9-12