MA 229 Notes Day 01

# Coordinatization of vectors

In the previous set of notes, we introduced the idea of arrow vectors and coordinate vectors. Now it's time to show an important relationship between the two. In particular, we can find a systematic way of turning arrow vectors into coordinate vectors in a way that preserves addition and scaling. This is called the standard coordinatization of the arrow vector.

## Standard coordinatization in 2 dimensions

The standard coordinatization describes how to start with an arrow vector and turn it into a coordinate vector.

To accomplish this, we first place the arrow vector on the \$xy\$-plane so that its tail is at the origin. Then, of course, its head will occur at some other point. The \$x\$ coordinate of this point becomes the 1st coordinate of the coordinate vector we are producing, and the \$y\$ coordinate becomes the second.

[[ Example of the standard coordinatization of an arrow vector ]]

That is, if we turn an arrow vector into a coordinate vector and then scale it, the result will be the same as if we had scaled it first and then turned it into a coordinate vector. Likewise, adding two arrow vectors together and then turning them into