In the wider theory of vectors, the scalar product is often called internal product, and dot product too. In other words, the scalar product is the product of the length of the first vector and the length of the projection of the second vector at first, as seen in the figure 1. 1 Scalar product The scalar product of two vectors, two oriented segments, a and b is a scalar a ⋅ b = ab cos γ, (1) where a = a and b = b are the intensities (lengths) of these vectors, and γ = ∠(a, b) is the angle between them. The text is an easier excerpt of the book of Quantum Mechanics, which this article is a promotion. Download Classical mechanics 3e by herbert goldstein solution manual and more Physics Exercises in PDF only on Docsity Goldstein Classical Mechanics Notes Michael Good 1 Chapter 1: Elementary Principles 1.1 Mechanics of a Single Particle Classical mechanics incorporates special relativity. Other multiplications have more vectors and are defined by the preceding ones, aggregating the factors as additional vectors. We will consider them mainly geometrically, together with the 'communicator multiplication' – my private from the same group. The two multiplying of the first group are the scalar and vector product – named according to the results, or the dot and a cross product of the vector – called according to the operation signs.
Mathematics knows a several ways the multiplication of two, three or more vectors, all explained here.
