Plane and Normal Vectors: Geometric Intuition in 3D

① This example demonstrates how a plane in 3D space is determined by a point and a normal vector, visually linking the plane equation with its normal vector. ② Core mathematical concepts include the point-normal form of a plane equation, normal vectors, vector operations, and the correspondence between planes and vectors in spatial geometry. ③ Construction highlights: Based on the construction summary, the GeoGebra command Vector is used, along with objects eq1 (plane equation), point P, and vectors u and v, to define the normal vector and associate it with the plane equation, creating a visual model of the plane and its normal. ④ Suitable for high school solid geometry or college analytic geometry courses, helping students understand the geometric meaning of the normal vector in plane equations and how to derive algebraic expressions from geometric objects. It is also useful for teacher demonstrations or student self-exploration.