Visualizing Vector Addition
vectors vector add addition order head tail matter visualization
One of the most basic laws about adding numbers is that if A + B = C, then B + A = C is also true. Likewise, if A + B + C = D, then A + C + B = D, and B + A + C = D, and B + C + A = D, and C + B + A = D, and C + A + B = D. No matter which order you add the numbers, they always add up to D.
The same rule holds true when adding Vectors (groups of numbers). The way you add vectors is you take the first components and add them together to produce the first component of the resulting vector, take the second components of the vectors and add them together, and continue until all components are added. Vectors are commonly only 2 component or 3 component, to represent points in 2D (flat) and 3D space, but they can be more. To add (6, 2) with (11, 3), the result is (6 + 11, 2 + 3) or (17, 5).
Now comes the fun part, visualization. This first picture shows 4 two-dimensional vectors, all coming from the origin (point (0, 0)).
E, which is the result of the addition. This visualization trick works in 3D as well as 2D.
Copyright 1998-1999 by Seumas McNally.
No reproduction may be made without the author's written consent.
Courtesy Of Longbow Digital Artists