A tool for determining the equation of a plane perpendicular to a given vector at a specific point is fundamental in vector calculus and related fields. For example, given a surface defined by a vector-valued function, this tool can find the plane tangent to a specific point on that surface. This plane is defined by its normal vector, which is perpendicular to the surface at the point of tangency.
Determining this perpendicular plane is crucial for applications in various fields, including computer graphics, collision detection in physics engines, and engineering design. Historically, these calculations were performed manually, a tedious and error-prone process. The development of computational tools streamlined this task, enabling more complex and accurate analyses. These tools are integral to modern 3D modeling and simulation software.