Vector Parametrization of a Line

① This example demonstrates how a line in 3D space can be described by a fixed point and a direction vector, with a parameter t controlling the position of any point on the line. ② Core mathematical concepts include vectors, parametric equations, direction vectors, position vectors, and the geometric meaning of the parameter t, forming a foundation for analytic geometry in three dimensions. ③ Construction details: using GeoGebra commands such as Intersect to find intersection points, Vector to create vectors, and Line to construct the line; objects include points A and B, direction vector u, moving point P, reference point P0, vector w, parameter t, line a, and function f (possibly for auxiliary display). ④ Suitable for high school or early university students learning vector geometry and spatial line equations, and for teachers demonstrating how parameter changes affect point positions on a line.