Orthonormal Basis in 3D Space

This lecture covers the concept of orthonormal bases in 3D space, where a basis is considered orthonormal if its vectors are pairwise orthogonal and have unit length. The lecture presents propositions and consequences related to orthonormal bases, including the formula for the scalar product and the distance between points in space. It also discusses the equation of a plane in 3D space and how to determine the distance of a point to a plane. The lecture concludes with the characterization of points in half-spaces relative to a plane, based on the signs of specific expressions.