Adding Vectors

We have seen how easy it is to add and subtract vectors in the same direction. To add vectors together which are at right angles to each other is easy too using Pythagoras. To find the angle of the resultant vector is easy too using simple trigonometry.

Consider this example;

A hiker walks 10km North then 5km East. How far from his starting point is he?

Draw a diagram where the vectors you want to add are put one after the other. Draw another arrow from the start to the end. This is the resultant, i.e. the sum of the two vectors.

What if the vectors aren't at right angles to each other?

Well there are two ways to solve this kind of problem:

1. We can draw a scale diagram

This method can be used for any number of vectors ( we then have a polygon ) but obviously its accuracy is limited.

2. We can resolve each vector into mutually perpendicular components and the use Pythagoras.
We see how to do this on the next page.