Question

Точки M N K лежат в двух различных плоскостях. Докажите что эти точки лежат на одной прямой.

Answer 1

Через три точки, не лежащие на одной прямой, можно провести ровно одну плоскость. Значит, три точки, не лежащие на одной прямой, не могут лежать в двух различных плоскостях. Из этого следует, что три точки из условия лежат на одной прямой, что и требовалось.

Answer 2

Proof that Points M, N, and K Lie on the Same Line

To prove that points M, N, and K lie on the same line, we can use the concept of collinearity. Collinearity refers to the property of points lying on the same line.

Let's assume that points M, N, and K do not lie on the same line. This means that they are not collinear. In order to prove that they are collinear, we need to show that there exists a line that passes through all three points.

We can use the following steps to prove the collinearity of points M, N, and K:

1. Assume that points M, N, and K do not lie on the same line. 2. Consider the plane in which points M and N lie. Since M and N are in the same plane, there exists a line that passes through these two points. 3. Now, consider the plane in which points N and K lie. Since N and K are in the same plane, there exists a line that passes through these two points. 4. Since both lines pass through point N, they must intersect at this point. 5. Therefore, there exists a line that passes through points M, N, and K, which means that the points are collinear.

Based on the above reasoning, we can conclude that points M, N, and K lie on the same line.

Please note that the specific coordinates or geometric properties of the points M, N, and K were not provided in the question. Therefore, the proof is based on the assumption that the points are not collinear and the general concept of collinearity.