Vector Decomposition: Scalar and Vector Products

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Page 3 of 3

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

Introduces scalar product, parallelism of vectors, and rate of change of a product.

Covers the concept of the mixed product and related vector identities.

Covers the properties of vectors, including commutativity, distributivity, and linearity.

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

Explores indicial notation, vectors, and the transformation law in the context of mass flux density.

Covers the concepts of dot and cross products of vectors and their applications.

Explores orthogonal and orthonormal bases, Gram-Schmidt process, and orthogonal polynomials in physics.

Explores the derivative of a product of functions and discusses algebraic products and scalar products of functions.

Covers the vector product in physics, explaining its properties and applications in 3D space.