From the diagram, we can see that represents a movement which can be described as:
Move 1 unit to the right and 3 units down.We can write this asSimilarly represents the movement:
Move 2 units to the right and 2 units upor:We add two movement (or displacement) vectors together using an ordinary sign, by thinking of as representing the phrase 'and then'. So means
Move 1 unit to the right and 3 units downwhich is obviously equivalent to
and thenMove 2 units to the right and 2 units up
Move 3 units to the right and 1 unit downWe sometimes write all of this as:Do you see how it works?
Now stands for:
Move from to So if and we must start at the point , and carry out the movement . When we do this, we get to the point . So that's where is: .
Now is the same movement as , but multiplied by . In other words:So:
and this is the movement . So, to find the position of the point , start at and carry out the movement . Can you see that is at ? (Check this carefully!)