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Many of you will know a good deal already about Vector Algebra — how to add and subtract vectors, how to take scalar and vector products of vectors, and something of how to describe geometric and physical entities using vectors.
Our basic unit types (dimensions) are length (L), time (T) and mass (M). When we do dimensional analysis we focus on the units of a physics equation without worrying about the numerical values.
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.
these units can be used to describe other physical quantities such as velocity (m/s), and acceleration (m/s2). Sometimes the string of units gets to be so long that we contract them into a new unit called a derived unit. For example, A unit of force has base units of kg m s2! newton or N where the newton (N) is a derived unit. 3.1 Physical ...
1.3 Unit vectors. 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.
The mathematicians have come up with a special kind of vector called a unit vector which comes in very handy in physics. By definition a unit vector has magnitude 1, with no units. By convention, a unit vector is represented by a letter marked with a circumflex. The circumflex is an accent mark that appears above the letter.
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.
