Question

If the three-dimensional space considers a cube Q and a plane P passing through 4 vertices of the cube that do not belong to the same measure of the edge of the cube is 1, then the intersection between the cube and plane is:

a) Empty set
b) A point
c) A line segment
d) A plane

Answer 1

The intersection between a cube and a plane passing through four vertices not on the same face is a line segment.

Step-by-step explanation:

If a plane P passes through 4 vertices of a cube Q that do not belong to the same face (given that the edge of the cube is 1), then the intersection between the cube and the plane is not an empty set, not a single point, nor a complete plane.

Considering the spatial structure of a cube, any plane passing through four non-coplanar points (vertices in this case) will intercept the cube in a four-sided figure, specifically, a tetrahedron. Thus, the correct answer is that the intersection is a line segment.