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A unit vector (sometimes called versor) is a vector with magnitude equal to one. e.g. Three unit vectors defined by orthogonal components of the Cartesian coordinate system: z. k. i = (1,0,0), obviously jij = 1. j = (0,1,0), jjj = 1. k = (0,0,1), jkj = 1. O.
Example. Write the polar unit vectors r and θ in terms of the Cartesian unit vectors x and y . Unit Vectors. We are familiar with the unit vectors in Cartesian coordinates, where . points in the x-direction and . y-direction.
Galileo Galilee. 3.1.1 Introduction to Vectors. Certain physical quantities such as mass or the absolute temperature at some point in space only have magnitude. A single number can represent each of these quantities, with appropriate units, which are called scalar quantities.
Let xˆ be a vector of unit magnitude pointing in the positive x-direction, yˆ, a vector of unit magnitude in the positive y-direction, and zˆ a vector of unit magnitude in the positive z-direction. Then xˆAx is a vector with magnitude equal to |Ax| and in the x-direction. By vector addition, A =xˆAx +yˆAy + ˆzAz. (1.5)
CONTENTS. A. Scaling a vector 321. :::::::::::::::::::::::::::::::::::::::::::::::: A. Unit or Direction vectors 321. :::::::::::::::::::::::::::::::::::::: A. Vector addition 322. ::::::::::::::::::::::::::::::::::::::::::::::::: A. Vector subtraction 322. :::::::::::::::::::::::::::::::::::::::::::::
Introduction to vectors. A vector is a quantity that has both a magnitude (or size) and a direction. Both of these properties must be given in order to specify a vector completely. In this unit we describe how to write down vectors, how to add and subtract them, and how to use them in geometry.
A unit vector is a dimensionless vector one unit in length used only to specify a given direction. Unit vectors have no other physical significance. In Physics 2110 and 2120 we will use the symbols i, j, and k (if there is a third dimension, i.e a “z” direction), although in many texts the symbols x^, y^, and z^ are often used.
