Intro to Scalar Multiplication of Vectors

① This GeoGebra example visually demonstrates the effect of multiplying a vector by a scalar, showing how the vector's length scales while its direction either remains the same or reverses for negative scalars. ② The core mathematical concept is scalar multiplication (scaling) of vectors, involving magnitude changes, direction preservation or reversal, and the role of the scalar coefficient. ③ Construction details: The Vector command is used with objects O (origin), A (point), u (vector from O to A), α (a slider-controlled scalar), and w (the resulting vector from O to α times u). Dragging the slider α allows real-time observation of how w changes. ④ This is ideal for high school or early college students learning linear algebra, serving as an introductory interactive tool for understanding the geometric meaning of vector scaling, and can be used in classroom demonstrations or independent exploration.