Geometric Demo of Vector Scalar Multiplication: Stretching and Reversing

This GeoGebra example demonstrates how vector scalar multiplication affects both magnitude and direction in the plane. By changing the scalar, the resulting vector is stretched or shrunk along the original direction; using a negative scalar flips the direction. The key mathematical ideas are vectors, scalar multiples, the geometric meaning of a vector’s length (magnitude), and direction, interpreted through position/vector construction. Construction focuses on using the Vector command to create the involved vectors (such as forming the base vector v from points A and B, building additional vectors like t and the scaled result v_1), along with text objects (text1, text2) to label proportions and outcomes. Buttons (button1, button2) support switching between cases so learners can visually track how v transforms under different scalar values. Suitable for middle school through early university levels, especially for introducing vector operations and building intuition for linear relationships.