Perpendicular Vectors: Constructing Orthogonality with Vector and Angle Commands

① This example demonstrates how to construct two perpendicular vectors in GeoGebra and visually verify that the angle between them is 90 degrees. ② The core mathematical concept is the perpendicularity of vectors, which can be checked via a zero dot product or a right angle; it also involves vector representation by start and end points and angle measurement. ③ Construction highlights: use the Vector command to create vector u (from u_start to u_end) and vector v (from v_start to v_end), use the Angle command to display the angle θ between them, and include a calculation to confirm orthogonality; objects include u_end, u_start, u, v_start, v_end, v, a, b, c, d, θ, e. ④ Suitable for high school or early college analytic geometry and vector lessons, useful for demonstrating the definition, verification, and dynamic adjustment of perpendicular vectors.