Resolving

If two vectors at right angles can be added together to form one vector can vectors be split up into components at right angles to each other?

 

The components of the vector F are Fx in the x direction and Fy in the y direction. 

If we were to add these two components together again we would end up with F.
Simple trigonometry ( remember SOH CAH TOA ) gives us the magnitude of the components..
... and we know the relationship between the angle and these components.

so the components of a vector F are Fx = F cosŲ  and Fy = F sinŲ

Be careful where the angle is. (you should ALWAYS draw a sketch and indicate the angle you are using). If the angle is between the vector and the component you are interested in then it's cos, if not it's sin.

consider this example;

A hiker walks 20km in a direction 350 East of North. How far North is he from his start? How far east?

Now that we can split a vector into its components at right angles to each other we can add together any number of vectors at any angle.