Math Problem Statement
Solution
The question in the image is in Ukrainian and reads:
"Пряма лежить у площині і перетинає площину . Яке взаємне розташування площин і ?"
Translated to English:
"A line lies in the plane and intersects plane . What is the mutual arrangement of the planes and ?"
The answer choices are:
- Площини не перетинаються (The planes do not intersect)
- Визначити неможливо (It is impossible to determine)
- Перетинаються по деякій прямій (They intersect along a line)
- Мають одну спільну точку (They have one common point)
- Площини збігаються (The planes coincide)
Explanation:
- Since line lies in plane and intersects plane , the two planes and must intersect. Typically, when two planes intersect, they do so along a line.
Thus, the correct answer is: Перетинаються по деякій прямій (They intersect along a line).
Would you like further details or clarifications?
Here are 5 related questions to deepen understanding:
- What are the conditions for two planes to intersect along a line?
- What happens geometrically when two planes have one common point?
- How do we determine if two planes coincide in three-dimensional space?
- How can we mathematically express the intersection of two planes using their equations?
- How can a line being in one plane and intersecting another affect the mutual arrangement of the planes?
Tip: In 3D geometry, two distinct planes that intersect do so along a line unless they are parallel or coincide.
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Math Problem Analysis
Mathematical Concepts
Plane Geometry
3D Geometry
Formulas
Equations of Planes in 3D Space
Theorems
Intersection of Planes
Suitable Grade Level
Grades 10-12
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