bivectorElement

A bivectorElement is a mathematical construct used in geometric algebra. It represents a planar orientation and magnitude within a multivector. A bivector is formed by the geometric product of two vectors, and a bivectorElement is essentially one of the components of a bivector, representing a specific oriented plane. In a 3D Euclidean space, a bivector can be thought of as having three fundamental bivectorElements, often associated with the coordinate planes: xy, yz, and zx. These elements are analogous to vectors in that they possess magnitude and direction, but their direction is planar. The geometric product of two vectors, for example, a * b, results in a bivector which can be decomposed into a scalar part and a bivector part. The bivector part is what is comprised of bivectorElements. These elements are crucial for representing rotations, areas, and other geometric operations in a unified framework. Understanding bivectorElements is fundamental to comprehending the applications of geometric algebra in fields such as physics, computer graphics, and engineering, where they provide a powerful way to describe and manipulate geometric quantities.