Equilateral Triangles and Parametric Curves of Vectors

Create a 2D coordinate-geometry diagram illustrating the relationship between vectors and equilateral triangles. Construct an equilateral triangle in the plane, then represent the triangle’s vertices and edges using 2D vectors to show their positions and directions. Add parametric curves (parameterized trajectories) that trace how these vector-defined vertices and edges move in the plane. Focus on the equilateral-triangle properties, the role of 2D vector operations in updating vertex/edge positions, and the visualization of those vector behaviors through parametric curve representations. Build the equilateral triangle first, then link the vector constructions with the corresponding parametric curves to display the relationship.