HP 48gII hp 48gII_user's manual_English_E_HDPMSG48E67_V2.pdf - Page 276

Chapter 9 Vectors This Chapter provides examples of entering and operating with vectors, both mathematical vectors of many elements, as well as physical vectors of 2 and 3 components. Definitions From a mathematical point of view, a vector is an array of 2 or more elements arranged into a row or a column. These will be referred to as row and column vectors. Examples are shown below: − 1 v =   3 , u = [1,− 3,5, 2]  6  Physical vectors have two or three components and can be used to represent physical quantities such as position, velocity, acceleration, forces, moments, linear and angular momentum, angular velocity and acceleration, etc. Referring to a Cartesian coordinate system (x,y,z), there exists unit vectors i, j, k associated with each coordinate direction, such that a physical vector A can be written in terms of its components Ax, Ay, Az, as A = Axi + Ayj + Azk. Alternative notation for this vector are: A = [Ax, Ay, Az], A = (Ax, Ay, Az), or A = < Ax, Ay, Az >. A two dimensional version of this vector will be written as A = Axi + Ayj, A = [Ax, Ay], A = (Ax, Ay), or A = < Ax, Ay >. Since in the calculator vectors are written between brackets [ ], we will choose the notation A = [Ax, Ay, Az] or A = [Ax, Ay, Az], to refer to two- and three-dimensional vectors from now on. The magnitude of a vector A is defined as |A| = Ax2 + Ay2 + Az2 . A unit vector in the direction of vector A, is defined as eA = A/|A|. Vectors can be multiplied by a scalar, e.g., kA = [kAx, kAy, kAz]. Physically, the vector kA is parallel to vector A, if k>0, or anti-parallel to vector A, if k