Unit Tangent, Normal, and Binormal Vectors on a Curve

This example demonstrates how to construct and visualize the unit tangent, unit normal, and unit binormal vectors along a curve (the Frenet-type local orthonormal frame). It focuses on the geometric idea that derivatives of a parameterized curve determine the tangent direction, the change of the tangent determines the normal direction, and the binormal direction is obtained from the cross product of the tangent and normal. In GeoGebra, the construction starts with CurveCartesian to define a curve object (A). Then Vector is used to create vector objects (a, u, v, w) representing the tangent/normal/binormal-related directions. Additional equations or constraints (eq1, eq2) enforce the intended relationships, such as normalization to unit vectors and consistent orientation. The model is well-suited for students studying calculus and vector geometry, especially parametric curve properties and the local behavior of space curves.