This lecture introduces the concepts of 'size' and 'distance in R^2 and R^m', focusing on orthogonal vectors and the least squares method. It covers the scalar product, unit vectors, and the Pythagorean theorem. The instructor explains the normalization of vectors, the distance between points, and the notion of perpendicularity in R. The lecture concludes with the definition of orthogonality and the proof of the Pythagorean theorem in R^m.