https://file.aiquickdraw.com/mathbot/file/1726762096689clx8wol9.jpg

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.

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### 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.

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

Understand how many planes perpendicular to a given plane can pass through a point that does not lie on the plane. This problem covers key 3D geometry concepts, including the uniqueness of perpendicular planes and geometric relationships in space. Suitable for students in Grades 9-12.

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