Vector Projection: Geometric Construction and Visualization

① This GeoGebra example dynamically demonstrates the projection of one vector onto another, visually illustrating the geometric meaning of the projection vector. ② Core mathematical concepts include the dot product, projection formula, orthogonal decomposition, and the relationship between the angle and projection length, with additional elements such as ellipse, geometric mean, and logarithmic functions for extended exploration. ③ Construction details: using commands Line, Vector, OrthogonalLine, Intersect, Angle, and Segment, the objects C, B, A, c, v, a, E, u, α, text1, text1_1, b, β, text2, and w are created; the orthogonal line determines the perpendicular foot, intersection marks the projection point, angle tool measures the angle, and segments represent the projection vector. ④ Suitable for high school or early college vector lessons, geometric construction practice, and dynamic math experiments to deepen understanding of both algebraic and geometric aspects of projection.