Interactive Vector Equation of a Line in 3D

This GeoGebra example dynamically illustrates the vector equation of a line in three-dimensional space, showing how any point on the line is generated by a position vector plus a scalar multiple of a direction vector. The core mathematical concepts include vectors, parametric equations, 3D coordinate geometry, and the relationship between lines and planes. The construction uses the Vector command to define the direction and position vectors, the Line command to draw the line, and Textfield/InputBox controls to adjust the parameter t, the initial point coordinates, and the direction vector components, allowing real-time observation of point P moving along the line. It is suitable for senior high school or early university students learning spatial analytic geometry, and also serves as an effective classroom demonstration tool for teachers to explain the geometric meaning of the parameter t in the vector equation.