Lecture

Analytical Study of Plan: Points, Lines

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Covers landmarks, coordinate systems, frames, and terminology in coordinates, emphasizing geometric angles and orthogonal vectors.

Covers calculations in coordinates for vectors, including bases, scalar product, and determinants, with geometric interpretations and examples.

Explores landmarks, coordinates, vectors, coplanarity, Cartesian equations, and geometric rules in space.

Covers the analytical study of space, focusing on points, lines, and planes.

Covers the analytical study of lines in a plane, focusing on equations and geometric interpretations.

Explores parametric equations, vectors, medians, landmarks, and Cartesian equations of lines in the plane.

Covers 3D orientation, cross product, and volume calculations using mixed product in vector calculus.

Covers examples of relative positions in a 2D space, focusing on equations involving x and y coordinates.

Introduces Cartesian equations of planes in space and their parametric representations.

Explores parametric equations in 2D coordinates and their geometric interpretations in different reference frames.

Covers orthogonality, scalar products, orthogonal bases, and vector projection in detail.

Covers vector spaces, bases, and decomposition of vectors in R³.

Covers the definition and use of coordinate systems and applications in bases and linear equations.

Covers the theorems related to orthogonal projection and orthonormal bases.

Explores coordinate vector operations, from digitizing points to transforming and manipulating geometric spaces using coordinates.

Covers linear equations, vectors, and matrices, exploring their fundamental concepts and applications.

Explores rotating vectors in physics, emphasizing the norm-angular speed relationship and various coordinate systems.

Covers linear independence, bases, and coordinate systems with examples and theorems.

Introduces orthogonality between vectors, angles, and orthogonal complement properties in vector spaces.

Explores vector and normal equations, covering lines, intersections, and distances in 2D and 3D geometry.