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alt="images"/>, i.e. if |q| = |p| and θpq = θpp = 0, then images. Hence, the magnitude of a vector images can also be expressed as

      (1.14)equation

      1.3.2 Cross Product

      The cross product (a.k.a. vector product) of two vectors images and images is denoted and defined as follows:

      In Eq. (1.15), as defined before, θpq is the angle measured from images to images. As for images, it is defined as a unit vector, which is perpendicular to the plane images formed by the vectors images and images.

      The sense of images is defined conventionally by the right‐hand rule. This rule is based on the right hand in such a way that images assumes the orientation of the thumb (directed from root to tip) while the fingers are oriented from images to images.

      Since, by definition, images and images, the following equations can be written for the vectors involved in the cross product.

      (1.16)equation

      (1.17)equation

      If sin θpq = 0, i.e. if images with θpq = 0 or images with θpq = π, then

      (1.18)equation

      If the order of images and images is reversed, Eq. (1.15) becomes

      (1.19)equation

      According to Eq. (1.12), θqp = θpq. However, according to the right‐hand rule,

      (1.20)equation

      Therefore, images. This verifies the well‐known characteristic feature of the cross product that its outcome changes sign when the order of its multiplicands is reversed. That is,

      (1.21)equation

Vector diagram of a reference frame.

      In Eq. (1.22), A is the origin of images. The origin of images may also be denoted as Oa. The coordinate axes of images are oriented so that each of them is aligned with one member of the following set of three vectors, which is denoted as images and defined as the basis vector triad of Скачать книгу