ortogonaalien

Ortogonaalien is a Finnish term that translates to "orthogonal" in English. It refers to a fundamental concept in mathematics and physics, particularly in geometry and linear algebra. Two objects, such as lines, vectors, planes, or surfaces, are considered orthogonal if they intersect at a right angle. This means the angle between them is 90 degrees or pi/2 radians.

In geometry, perpendicular lines are a common example of orthogonal objects. In three-dimensional space, a line can be orthogonal to a plane if it is perpendicular to every line within that plane that passes through the point of intersection. This concept extends to higher dimensions, where orthogonality is defined using dot products. For two vectors, their dot product is zero if and only if they are orthogonal.

The principle of orthogonality is crucial in various fields. In linear algebra, orthogonal bases simplify many calculations and representations of vector spaces. In physics, orthogonal components are often used to decompose forces, velocities, or electric and magnetic fields, making analysis more manageable. For instance, the Cartesian coordinate system is based on three mutually orthogonal axes. The term "ortogonaalien" therefore encapsulates this important property of perpendicularity and its widespread application.