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Unit Vectors. We are familiar with the unit vectors in Cartesian coordinates, where . points in the x-direction and . y-direction. Here, we will first state the general definition of a unit vector, and then extend this definition into 2D polar coordinates and 3D spherical coordinates. 2D Cartesian Coordinates. Consider a point (x, y).
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.
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.
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.
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 z ˆ a vector of unit magnitude in the positive z - direction.
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.
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 ...
