Ortogonal vs. perpendicular
The Spanish words 'ortogonal' and 'perpendicular' are often used in geometry and other contexts to describe angles and relationships between lines or planes. While they are related, they are not always interchangeable.
Ortogonal
Ortogonal refers to the relationship between lines or vectors that meet at a right angle (90 degrees). In a broader sense, it implies orthogonality, which can also pertain to concepts in higher-dimensional spaces and even functional spaces in advanced mathematics.
Los ejes X y Y en un plano cartesiano son ortogonales.
(The X and Y axes in a Cartesian plane are orthogonal.)
En álgebra, dos vectores son ortogonales si su producto punto es cero.
(In algebra, two vectors are orthogonal if their dot product is zero.)
Perpendicular
Perpendicular refers specifically to the relationship between two lines that intersect at a right angle (90 degrees). This term is commonly used in everyday language and basic geometry to describe this intersection.
Los lados de un cuadrado son perpendiculares entre sí.
(The sides of a square are perpendicular to each other.)
Dibuja una línea perpendicular desde este punto en el círculo.
(Draw a perpendicular line from this point on the circle.)
Summary
In summary, while both 'ortogonal' and 'perpendicular' describe relationships involving right angles, 'ortogonal' is a broader term that can apply to higher dimensions and functional spaces. In contrast, 'perpendicular' is typically limited to basic geometrical contexts involving intersections at right angles.