Lecture

Analytical Geometry: Vectors

Related lectures (29)

Introduces vector definitions, displacement, addition, and applications in geometry.

Analytical Geometry: Vector Equations of Lines

Covers vector equations of lines in analytical geometry, including finding intersection points and orthogonal projections.

Linear Dependence of Vectors

Explores linear dependence of vectors, demonstrating examples and conditions for collinearity.

Analytical Geometry: Vectors and Operations

Covers the fundamentals of analytical geometry, focusing on vectors and their operations.

Vector Geometry: Basics and Applications

Explores vector geometry basics, historical perspectives, and practical applications.

Vectors: Fundamentals

Covers the basic concepts related to vectors, including their definition, operations, and properties, as well as applications through examples and the Varignon's theorem.

Elementary Operations in Geometry

Explores elementary operations in geometry, including addition, subtraction, multiplication, and division of segments and angles.

Analytical Geometry: Lines Study

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

Orthogonality and Least Squares Method

Covers orthogonal vectors, unit vectors, and the Pythagorean theorem in R^m.

Analytical Geometry: Cross Product and Orientation

Explains the cross product in analytical geometry and vector orientation.

Elements of Lie Groups and Algebras

Explores the transformation of vectors and tensors in quantum physics, emphasizing Lie groups and algebras.

Translations and Homotheties

Covers translations, homotheties, and their geometric properties, including reversibility and composition.

Scalar Products in 2D and 3D Geometry

Explores the scalar product, vector lengths, angles, norms, and rotations in 2D and 3D spaces.

Analytical Geometry: Symmetry of Vectors

Explores the symmetry of vectors with respect to a line in Analytical Geometry.

Orthogonal Projections: Rectors and Norms

Covers orthogonal projections, rectors, norms, and geometric observations in vector spaces.

Analytical Geometry: Oriented Angles

Explores oriented angles in analytical geometry, discussing unit vectors, trigonometric functions, matrix representations, and rotations.

Vectors and Kinematics

Introduces vectors in a solid reference frame and explains the importance of determinants in interpreting vector products and coordinate changes.

Homotheties and Translations

Explores homotheties and translations in geometry, focusing on preserving alignment and distances.

Translations and Homotheties

Explores translations and homotheties, discussing their properties and practical applications in preserving geometric characteristics.

Analytical Geometry: Bisectors and Areas

Explores the properties of bisectors and areas in Analytical Geometry.