perpendicularmente

Perpendicularmente is an adverb used to describe an action or relation that occurs at a right angle to a line, plane, or direction. In mathematical and technical language, it characterizes how one object relates to another with a 90-degree relationship. For example, a sentence such as "La recta AB corta perpendicularmente a la recta CD" indicates that AB intersects CD forming a right angle.

In geometry, two lines are perpendicular if they intersect and the angle between them is 90 degrees. This can be tested with slopes: if neither line is vertical, the product of their slopes m1 and m2 equals -1. If one line is vertical, the other must be horizontal to be perpendicular. In three-dimensional space, a line is perpendicular to a plane if it is perpendicular to every line in that plane that passes through their point of intersection. Perpendicular relationships also extend to vectors: two nonzero vectors are perpendicular when their dot product is zero, indicating orthogonality.

Usage and terminology vary by language: perpendicularmente is common in Spanish and Portuguese to form adverbial phrases, while English typically uses perpendicularly. The concept underlies notions such as normal vectors, orthogonality, and right angles, and it plays a central role in constructions, measurements, and vector or coordinate calculations.

Related terms include perpendicular, orthogonal, right angle, normal, and the condition of perpendicularity in slopes, dot products, and geometric intersections.