HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 277

There are two definitions of products of physical vectors, a scalar or internal product (the dot product) and a vector or external product (the cross product). The dot product produces a scalar value defined as A•B = |A||B|cos(θ), where θ is the angle between the two vectors. The cross product produces a vector A×B whose magnitude is |A×B| = |A||B|sin(θ), and its direction is given by the so-called right-hand rule (consult a textbook on Math, Physics, or Mechanics to see this operation illustrated graphically). In terms of Cartesian components, A•B = AxBx+AyBy+AzBz, and A×B = [AyBz-AzBy,AzBx-AxBz,AxByAyBx]. The angle between two vectors can be found from the definition of the dot product as cos(θ) = A•B/|A||B|= eA•eB. Thus, if two vectors A and B are perpendicular (θ = 900 = π/2rad), A•B = 0. Entering vectors In the calculator, vectors are represented by a sequence of numbers enclosed between brackets, and typically entered as row vectors. The brackets are generated in the calculator by the keystroke combination „Ô , associated with the * key. The following are examples of vectors in the calculator: [3.5, 2.2, -1.3, 5.6, 2.3] A general row vector [1.5,-2.2] A 2-D vector [3,-1,2] A 3-D vector ['t','t^2','SIN(t)'] A vector of algebraics Typing vectors in the stack With the calculator in ALG mode, a vector is typed into the stack by opening a set of brackets („Ô) and typing the components or elements of the vector separated by commas (,í). The screen shots below show the entering of a numerical vector followed by an algebraic vector. The figure to the left shows the algebraic vector before pressing „. The figure to the right shows the calculator's screen after entering the algebraic vector: Page 9-2