Three points D, E, and F are collinear. Is there only one plane that contains these three points?

No.

Consider the spine of your noteboook or the spine of a book.
all the pages fanned out would be different planes, but they would all pass through the same 3 points on the spine.

To determine if there is only one plane that contains three collinear points, we need to understand the concept of collinearity and the properties of planes.

Collinear points are points that lie on the same straight line. In this case, points D, E, and F are collinear. If three points are collinear, they can be thought of as lying on an imaginary line in space.

Now, let's consider the concept of a plane. A plane is a flat, two-dimensional surface that extends infinitely in all directions. It can be defined by any three non-collinear points.

Here's how to determine if there is only one plane that contains the collinear points D, E, and F:

1. If the three collinear points D, E, and F are the only points given, then they do not define a plane. In this case, there is no plane that contains these points.

2. If there are additional non-collinear points given along with D, E, and F, and a plane can be defined using any three non-collinear points from the given set of points, then there is only one plane that contains the collinear points.

To summarize, if the given points D, E, and F are the only points provided, then there is no plane containing them. However, if additional non-collinear points are given, a plane can be defined that contains all the points, and there will be only one such plane.