Читать книгу Kinematics of General Spatial Mechanical Systems - M. Kemal Ozgoren - Страница 18

The dot product (a.k.a. scalar product) of two vectors and is denoted and defined as follows:

(1.10)

In Eq. (1.10), θ_pq is defined as the angle between the vectors and . It is denoted as

(1.11)

Without any significant loss of generality, the range of θ_pq may be defined so that 0 ≤ θ_pq ≤ π. According to this range definition, it happens that

(1.12)

Besides, cosθ_pq is not sensitive to the sense of θ_pq anyway. Therefore, the order of the vectors in the dot product is immaterial. That is,

(1.13)

If , i.e. if is perpendicular (or orthogonal or normal) to so that θ_pq = π/2, then .

If , i.e. if |q| = |p| and θ_pq = θ_pp = 0, then . Hence, the magnitude of a vector can also be expressed as

(1.14)