# Why vector form is convenient?

by manimaran1605
Tags: convenient, form, vector
 Math Emeritus Sci Advisor Thanks PF Gold P: 39,682 Because there are many different points the same distance from the origin (or any one point) of a coordinate system so a single number will not suffice to identify it. Equivalently, it take 3 numbers to identify everypoint in a 3D coordinate system (pretty much the definition of "3D") and it is convenient to arrange those numbers in an array. It is the fact, from geometry of similar triangles, that the coordinates $(x_0, y_0, z_0)$ of a point exactly 1/2 way between two points $(x_1, y_1, z_1)$ and $(x_2, y_2, z_2)$ are $(x_0, y_0, z_0)= ((x_1+ x_2)/2, (y_1+ y_2)/2, (z_1+ z_2)/2)$ that means that "scalar multiplication" of vectors is convenient (in fact, "scalar multiplication" and the whole idea of vectors was created to simplify that). (Arildno got in two minutes before me! And we are saying essentially the same thing.)