what is noncoplanar points

The are not in the same plane.

Noncoplanar points refer to a set of points that do not lie on the same plane. In Euclidean geometry, a plane is a two-dimensional flat surface that extends indefinitely in all directions. When three or more points are coplanar, it means that they can be contained within the same plane. However, if a set of points is noncoplanar, it indicates that they cannot be all contained within a single plane and are instead located in different planes or positions in three-dimensional space.

To determine whether points are coplanar or noncoplanar, you can use the following method:

1. Consider a set of points and their coordinates (x, y, z).
2. Write the coordinates of the points in matrix form, where each point corresponds to a row or column in the matrix.
3. Calculate the determinant of the matrix. If the determinant equals zero, the points are coplanar; otherwise, they are noncoplanar.

If you are given the coordinates of three points (x₁, y₁, z₁), (x₂, y₂, z₂), and (x₃, y₃, z₃), you can write the matrix as:

| x₁ y₁ z₁ |
| x₂ y₂ z₂ |
| x₃ y₃ z₃ |

If the determinant equals zero, the points are coplanar. If the determinant does not equal zero, the points are noncoplanar.