Vector and Scalar Multiplication: A Geometric and Algebraic Demonstration

This example demonstrates the concept of multiplying a vector by a scalar, combining geometric and algebraic perspectives. Using GeoGebra commands such as Vector, objects like A, B, u, C, D, v, E, F, w, G, H, a, I, J, b, text1, text2, text3, text4, text5, text6, text7, text8, text9, k, K, L, c, d, M, text10, text11, text12, e, f, text13, text14, text15, text16, text17, illustrates how scalar multiplication affects vector length and direction. Key mathematical concepts include vector operations, proportional scaling, and coordinate transformations. Suitable for middle or high school students to understand vector basics and their applications in geometry and algebra.