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This lecture covers the analytical study of space, including landmarks, coordinates, vectors, coordinate systems, orthornormal bases, and Cartesian equations. It also explores the concept of coplanarity, calculation rules, and the relative position of lines in space. The lecture delves into the properties of coordinate systems, vector planes, and linear combinations. Additionally, it discusses the geometric rules for verifying angles and the relationship between vectors in space. The presentation concludes with examples illustrating the application of the concepts discussed throughout the lecture.