Scalar Product and Vectors

This lecture covers the components of a vector in a 3D orthonormal frame, the different conventions for writing vectors in components, the sum of two vectors, and the multiplication of a vector by a scalar. It also explains the concepts of colinear and coplanar vectors, linearly independent vectors, norm of a vector, scalar product, and vector product. The properties of scalar and vector products are discussed, including commutativity, distributivity, and independence of the reference frame. The lecture concludes with the rule of the right hand for vector products and useful vector identities.