Parametric Intersection of a Sphere and a Plane (Circle)

This example demonstrates how to construct and visualize the intersection curve (typically a circle) of a sphere and a plane in 3D space using parametric equations. Core mathematical concepts include spatial analytic geometry, sphere and plane equations, solving intersection of surfaces, and parametric curve representation. The construction uses GeoGebra commands such as Vector, Line, Intersect, Transpose, ReducedRowEchelonForm, UnitVector, and CurveCartesian to compute the foot of perpendicular from the sphere center to the plane, the distance, and orthonormal basis vectors within the plane, then generate the parametric circle. Suitable for senior high school or early university students learning spatial geometry and parametric equations, and for teachers demonstrating dynamic 3D intersections in class.