Verticality mathematically means that the intersection angle of two straight lines or planes is 90 degrees. This relationship has important applications in plane geometry, three-dimensional space geometry and vector algebra. The following is a specific explanation:

In plane geometry, verticality means that the intersection angle of two straight lines is 90 degrees. Vertical lines are usually used to indicate the shortest distance between the endpoints of two line segments. For example, in a rectangle, diagonal lines are perpendicular to each other. In a right triangle, the hypotenuse is also perpendicular to the base.

In three-dimensional space, verticality can refer to the relationship between planes or straight lines. The fact that two planes are perpendicular means that the included angle between them is 90 degrees. The verticality of two straight lines can be determined by calculating the dot product of their direction vectors. When the dot product is 0, two straight lines are perpendicular.

In vector algebra, verticality is defined as the dot product of two vectors being 0. If the dot product of two vectors is 0, then the angle between them is 90 degrees. This definition enables verticality to be extended to higher dimensional vector space. The concept of verticality is widely used in computer graphics, physics and engineering.