Vector Operations and Geometric Construction

①This GeoGebra example dynamically demonstrates basic vector operations (such as addition, scalar multiplication, or dot product) and their visual effects in plane geometry, involving two vectors u and v, along with intersection points and a general quadrilateral structure. ②Core mathematical concepts include linear operations on 2D vectors, collinearity and perpendicularity, applications of vectors in geometric figures (e.g., general quadrilaterals), and connections to complex number representation on the plane. ③Construction highlights: using the Intersect command to find intersection points of lines or curves, the Vector command to create vector objects, and setting points A, B, C and vectors u, v as fundamental elements, allowing interactive dragging to observe changes in operation results. ④Suitable for high school or early college mathematics instruction, ideal for classroom demonstrations or student self-exploration in vector chapters, helping to understand the geometric meaning and coordinate representation of vector operations.