Scalar Product of 3D Vectors Visualization

① This example demonstrates the scalar product (dot product) of two 3-dimensional vectors, showing both its numerical value and geometric interpretation as the vectors are dynamically adjusted. ② Core mathematical concepts include the definition of the dot product in 3D, the cosine formula relating dot product to the angle between vectors, and the projection interpretation of the scalar product. ③ Construction details: using GeoGebra commands such as Intersect to define vector endpoints, Vector to create vectors u and v, Angle to measure the angle α between them, and ScalarProduct to compute the dot product; points A, B, C can be dragged or sliders used to update the visualization in real time. ④ Suitable for senior high school or university courses in linear algebra, analytic geometry, or physics, helping students grasp the algebraic and geometric duality of the dot product and its applications in work and projections.