Column vectors and magnitude

Last time

Before we start: last time, in Transformations, you learned these points. Here they are again on one card. Keep them in mind, because today builds on them.

How far and which way

A pilot is told: fly four kilometres east and five north. That is a vector: a journey with a size and a direction. We write it as a column of two numbers. Adding vectors is joining journeys, and the magnitude is the length of the straight line from start to finish.

Column vectors

A column vector has two numbers. The top says how far across, the bottom says how far up. Positive across is right, negative is left. Positive up is up, negative is down. The vector three, two goes three right, two up. The vector minus one, four goes one left and four up.

Adding and subtracting

Let a be three, two, and b be minus one, four. To add, add the tops and add the bottoms. a plus b is three minus one, and two plus four: two, six. a minus b is three plus one, and two minus four: four, minus two.