In Euclidean geometry, we analyze the relationships and properties of space. One key concept is the idea of a plane, which is a flat, two-dimensional surface that extends infinitely in all directions.
When dealing with points in Euclidean space, it's important to understand the concept of collinearity. Points are collinear if they lie on the same straight line. Conversely, points that are not collinear do not lie on a single straight line.
The question asks how many planes can contain any three points that are not on the same line. Let's break this down step by step:
1. A plane in Euclidean space is defined by three points that are not collinear.
2. These three points determine a unique position in space, forming a single, specific plane.
3. No other plane can be formed with these three points that does not overlap or coincide with the original plane.
Given these points:
- If the three points are collinear, they lie on the same line, and an infinite number of planes could contain that line. However, this is not the case in our scenario since the points are not on the same line.
- Since the three points provided are not collinear, they must lie on exactly one unique plane.
Therefore, any three points not on the same line can lie on exactly one plane.
The correct answer is: one plane.
