Question

Пряма n, яка не лежить у площині трикутника АВС, перетинає його сторону ВС в точці К. 1) Чи може пряма n перетинати сторону АВ? Відповідь обґрунтуйте. 2) Яким є взаємне розміщення прямих n і АС?

Answer 1

1) Пряма n не може перетинати сторону АВ трикутника АВС, оскільки вона не лежить у площині цього трикутника.

2) Прямі n і АС можуть бути паралельними, оскільки обидві лежать у площині трикутника АВС і можуть не перетинатися.

Answer 2

Direct translation of the user's query:

Answer in detail. A line n, which does not lie in the plane of triangle ABC, intersects its side BC at point K. 1) Can line n intersect side AB? Justify your answer. 2) What is the mutual arrangement of lines n and AC?

Response:

To answer your questions, let's consider the given scenario:

1) Can line n intersect side AB? - No, line n cannot intersect side AB. This is because line n lies outside the plane of triangle ABC, and side AB lies within the plane of the triangle. Since line n does not lie in the same plane as the triangle, it cannot intersect any of the sides within the triangle's plane. Therefore, line n cannot intersect side AB. [[1]]

2) What is the mutual arrangement of lines n and AC? - Since line n does not lie in the plane of triangle ABC, it is not parallel to any of the sides of the triangle. Therefore, line n and line AC are not parallel. The exact relationship between line n and line AC cannot be determined without additional information. They could intersect at a point, be skew lines (lines that do not intersect and are not parallel), or have some other type of relationship. Without more information, we cannot determine the specific mutual arrangement of lines n and AC. [[1]]

I hope this clarifies your questions. Let me know if there's anything else I can help you with!