Visualizing the Span of Three Vectors by Katrina Palmer

① This example dynamically demonstrates the geometric shape of the linear span of three vectors u, v, and w in space by adjusting the coefficients c1, c2, c3. ② The core mathematical concept is the span in linear algebra—the set of all linear combinations c1·u + c2·v + c3·w, which can be a plane, a line, or the entire 3D space depending on linear dependence. ③ Construction: using GeoGebra's Vector command to define vectors u, v, w, and three sliders c1, c2, c3 as combination coefficients; animating the sliders updates the combined vector in real time, tracing the spanned region. ④ Suitable for senior high school or introductory university linear algebra, helping students visually grasp linear combinations, linear dependence, and basis, and explore how the dimension of the span changes with the vectors.