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Vector Calculus in 3D
This lecture covers the concept of 3D vector space, defining the set of vectors in space and the operations on them (scalar multiplication, addition, linear combinations). It explains the notion of a base in a vector space and the properties of orthonormal bases. The lecture also delves into the scalar product, presenting its definitions and results, and how to calculate it. It further explores the projection of vectors, orthogonality, and the representation of vectors in a base. The lecture concludes with examples and solutions illustrating the application of vector calculus in 3D space.