



Sometimes we need to add two vectors together. 


If we are very lucky, they will be heading in the same direction. 





In that case, we just add them together 


and the direction stays the same. 











That rarely happens. 





The next easiest case is if the vectors are headed 


in exactly the opposite direction.






In that case we just subtract the smaller one from the larger one. 


The direction of what's left is the same as the original larger one. 











So all of that is fine and pretty easy to deal with. 





But what if the two vectors are headed at crazy angles to each other? 





We can't easily add or subtract vectors 


unless they are pointing in the same or opposite directions. 


So we make the crazy angle vectors point in the same or opposite directions. 





We do that by dividing each vector into it's component parts 


that run along the X and Y axis. 





Then we can add or subtract the vectors that are along the same axis. 





Example: 





Say
we want to add together two vectors. 


One
goes for two miles 30° north of east (compass heading 60°). 


The
other one goes for two miles 45° north of east (compass heading
45°). 











If
we call North the positive Y direction, 


and
call East the positive X direction, 


the
components of the vectors are ... 











So
the sums of the component vectors 


in
the X (East) and Y (North) directions are ... 





X
= 1.732 mi + 1.414 mi = 3.146 mi



Y = 1 mi + 1.414
mi = 2.414 mi 





The
angle of this new combined vector can be found 


by
using the tangent function on these X and Y values ... 











We
really did just just place these vectors head to tail and add
them. 


But
doing it graphically just doesn't get you the length or angle. 











copyright 2005 Bruce Kirkpatrick 
