Parametric Equation of a 3D Line via Vectors

This example demonstrates how to construct and visualize a line in 3D using a parametric equation built from an initial point and a direction vector. The key mathematical ideas are parametric representation, vector form of a line in three-dimensional space, and linear geometric reasoning (turning linear constraints into a drawable locus). In the construction, objects such as A and O serve as reference points, while u provides the direction; a parameter (e.g., d) generates points P on the line, and text labels (text2/text4/text5) annotate important components. Using the GeoGebra commands Intersect and Vector, the model locates required geometric elements (e.g., intersections and vector-based construction steps), and CurveCartesian is used to render the parametric line as a visible curve in 3D. It is intended for learners studying coordinate geometry and solid geometry at the high-school to early-university level, especially when connecting vector methods with parametric equations and 3D graphing.