Vector Equation of a Line in 2D: r = a + λd

This interactive GeoGebra example demonstrates the vector equation of a straight line in two-dimensional space, written in parametric form as r = a + λd. It shows how the position vector r traces the line as the scalar parameter λ varies, with a representing a fixed point on the line and d representing the direction vector. Core mathematical concepts include 2D vectors, vector equations of lines, parametric equations, position vectors, direction vectors, and coordinate geometry. The construction relies on GeoGebra commands such as Intersect, Vector, Line, and FractionText, together with objects including points A, B, P, vectors a, d, u, scalar t, and multiple text labels for dynamic display. Suitable for high school analytic geometry and vector units, as well as introductory university courses on parametric curves, this resource supports classroom demonstration and student-led exploration of line geometry and linear motion.