Vector Addition

You can probably understand the idea if we show you examples:

(1,2) + (3,4) = (4,6)

\begin{bmatrix} 2 \\ 7 \end{bmatrix} + \begin{bmatrix} 3 \\ 1 \end{bmatrix} = \begin{bmatrix} 5 \\ 8 \end{bmatrix}

We want you to think of vector addition as a way of keeping track of separate processes.

A ladybug is on a train. The train is moving in the positive x direction and the ladybug is also moving in the positive x direction. The velocity of a train is 100 meters per second and the ladybug is walking with a velocity of 1 mm/s.

We need for both units to be the same so we change 1 mm/s to 0.001 meters per s.

The velocity of a train is 100 meters per second in the positive x direction. A ladybug is walking in the positive x direction at 1 mm/s.

1.001 m/s = 1 m/s + 0.001 m/s

The velocity of the ladybug is 1.001 m/s.

Appendix A

If we are only working with integers for our values of x and y, then we can add scaled copies of the vectors (1,0) and (0,1) to get (a,b).

a(1,0) + b(0,1) = (a,0) + (0,b) = (a,b)