The orthogonal complement of a subspace in a vector space consists of all vectors that are perpendicular to every vector in that subspace. For example, in a three-dimensional space, if you have a plane (the subspace), the orthogonal complement would be a line that is perpendicular to that plane. This concept is crucial in linear algebra and helps in understanding the relationships between different subspaces. Mathematically, if you have a subspace W of a vector space V, the orthogonal complement is denoted as W⊥. It includes all vectors v in V such that the dot product of v with any vector in W equals zero. This property is essential for solving systems of linear equations and for applications in areas like computer graphics and signal processing.