Tangent, Normal, and Binormal Vectors at a Point on a Curve

① This example visualizes a 3D parametric curve with its tangent, normal, and binormal vectors drawn at a movable point, forming the Frenet frame that shows local bending and twisting. ② Core math concepts include parametric space curves, unit tangent vector, principal normal, binormal (cross product), and the orthogonal Frenet-Serret frame. ③ Construction uses GeoGebra commands: CurveCartesian defines the curve a, Vector creates vectors, and UnitVector normalizes the tangent; objects include curve a, point A, vectors T (tangent), N (normal), B (binormal), plus auxiliary objects r, m, unittangent, b₂, C, v, u, etc., with dynamic updates via slider or moving point A. ④ Suitable for university calculus or differential geometry courses explaining space curve properties, and also for advanced high school math or teacher demonstrations of vectors and derivatives in 3D.