3D Golf Shot Trajectory: Vectors and Parabola

This example demonstrates a 3D “golf ball hit” scenario by visualizing the projectile trajectory of a ball in space and the geometric relationship between the path and the instantaneous direction (tangent). It highlights core ideas from analytic geometry and vector calculus in a purely geometric construction: vector components for velocity, a parabola as the path, tangent direction (tangent line/tangent behavior), and orthogonal planes to encode direction constraints. Construction-wise, it uses commands such as Intersect and OrthogonalPlane to define relevant orthogonal geometric sets, Vector to build direction/velocity vectors and their components, Translate to shift points/vectors to the moving configuration, and PointIn to bind the evolving ball position to the parameterized setup. Key objects include the ball representations (BALL, Ball′, Ball′_1), position points (Position), the origin (Origin), and the target area/point (HOLE), driven by a time parameter t. Suitable for high school advanced students and undergraduate introductory courses covering 3D geometry, vectors, and parameterized trajectory visualization.