Orthogonality is a concept used in various fields, primarily in mathematics, statistics, and computer science, which describes the idea of two vectors being perpendicular to each other in a specific space. In the context of Euclidean space, two vectors are said to be orthogonal if their dot product is zero.
Orthogonal coordinate systems are systems used to define a point in space using coordinates in such a way that the coordinate axes are perpendicular (orthogonal) to each other. In these systems, the position of a point is determined by a set of values, typically referred to as coordinates, which indicates its distance from the axes.
Orthogonal wavelets are a specific type of wavelet used in signal processing and data analysis that possess the property of orthogonality. Unlike other wavelet systems, where wavelets may not be orthogonal to one another, orthogonal wavelets are formed in such a way that they are mathematically independent. This has significant implications for data representation and processing.
In geometry, the term "normal" can refer to several concepts, but it is most commonly used in relation to the idea of a line or vector that is perpendicular to a surface or another line. Here are a few contexts in which "normal" is used: 1. **Normal Vector:** In three-dimensional space, a normal vector to a surface at a given point is a vector that is perpendicular to the tangent plane of the surface at that point.
The term "perpendicular" refers to the relationship between two lines, segments, or planes that meet or intersect at a right angle (90 degrees). In two-dimensional geometry, if line segment \( AB \) is perpendicular to line segment \( CD \), it means they intersect at an angle of 90 degrees. In three-dimensional space, the concept extends similarly; for example, a line can be said to be perpendicular to a plane if it intersects the plane at a right angle.
Perpendicular distance refers to the shortest distance from a point to a line, plane, or a geometric shape. This distance is measured along a line that is perpendicular (at a 90-degree angle) to the surface or line in question. ### Key Points: - **From a Point to a Line**: The perpendicular distance from a point to a line is the length of the segment that connects the point to the line at a right angle.
A rectangular cuboid, also known as a rectangular prism, is a three-dimensional geometric shape that has six rectangular faces. The key characteristics of a rectangular cuboid include: 1. **Faces:** It has six faces, all of which are rectangles. 2. **Edges:** There are twelve edges in total, with three pairs of parallel edges. 3. **Vertices:** It has eight vertices (corners) where the edges meet.
