3D Point, Vector and Plane Comprehensive Task

① This example demonstrates how to construct a complete geometric model in 3D space using points, vectors, and planes, including point positioning, vector translation, and orthogonal plane relationships. ② Core mathematical concepts involve 3D analytic geometry: point coordinates, vector operations, plane equations, orthogonal planes, and angle measurement in space, while also incorporating statistical elements like median line and standard deviation for interdisciplinary application. ③ Construction highlights: using GeoGebra commands such as Segment, Vector, Translate, OrthogonalPlane, PointIn, and Angle, it builds multiple points (A, X, Y, P, etc.), vectors (u, v, n, etc.), and planes (f, g, h, etc.), establishing spatial structure through translation and orthogonality, with objects including coordinate variables x₀, y₀, z₀ and auxiliary points O, N, B, C. ④ Suitable for high school or early college students to understand 3D spatial geometry concepts, and useful for teachers designing tasks on spatial vectors and planes, especially for cross-disciplinary exploration combining statistics and geometry.