Hello, I have a question about why the starting points of the Cartesian vectors in the example are not from the origin point (0,0) - does it matter where the vectors starting point begin? Can you arbitrarily make a starting origin point?

Thank you

Introduction In unit '1, we learned how to represent vectors geometrically as directed line segments. We can also draw vectors on a coordinate grid. If a vector is plotted on a (Cartesian) grid, it is called a Cartesian Vector. Denitions A Cartesian vector, E', is represented by an ordered pair in two-space or R2 (two- dimensional coordinate system). where E; and E; are called the components of vector i\". m: is the x-component (or horizontal component) of the vector E'. 1T; is the yoomponent (or vertical component] of the vector E'. E' = [$3, 11?] means starting at the tail, the head of E\" can be reached by moving [EH units to the right or left (move right if E; is positive, move left if negative) and [KM units up or down (move up if E; is positive and move down if it is negative). On the above diagram, 0 The head of E' is reached by moving 4 units right and 3 units up (starting at the tail). Therefore, _L at. = [4, 3]. The numbers 4 and 3 are called the components of H'. o The head of ' is reached by moving 2 units left and 3 units down. Therefore, ' = [2, 3]. o The head of is reached by moving 6 units right and 2 units down. Therefore, = [6, 2]. Note The square brackets are used for Cartesian vectors to distinguish it from ordered pairs that represent the points. (3, 5) ' Point [3, 5] d Cartesian Vector