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Feb 24, 2015 · Preliminaries. This tutorial will denote vector quantities with an arrow atop a letter, except unit vectors that define coordinate systems which will have a hat. 3-D Cartesian coordinates will be indicated by $ x, y, z $ and cylindrical coordinates with $ r,\theta,z $. 2) draw a vector pointing towards 2-oclock (so we have $\theta = 30$, this is arbitrary but I prefer this 30 degree angle as I tend to confuse the sin and cos on a 45 degree angle) with a length of 1, so this vector ($\vec{V}$) ends on the unit circle. Dec 31, 2012 · Hence the Pythagorean length of a vector is simply , and so we can find the inverse vector. (5) We define the distance measure or metric over the space as the scalar part of the geometric product, which for the special case of two vectors reduces to the dot product as shown in Eq. (3).