The Parallelogram Method

The parallelogram method is a little more difficult to describe, but is just as easy in practice as the head-to-tail method.  The best way to understand this method is to see it performed visually.

Examine the following applet and watch carefully as a parallelogram is formed by the two vectors being summed. 

Applet by Fu Kwun Hwang

Using the mouse, draw two vectors and watch the applet form the parallelogram.  Notice that the resultant vector points from where the tails are joined to the far corner of the parallelogram.

As I mentioned previously, the head-to-tail method and parallelogram method are identical.  This is especially obvious when summing two vectors. Using the above applet, sum two vectors and watch carefully.  Do you see how the parallelogram method naturally evolves into the head-to-tail method?  (Remember, for the purposes of summing, a vector can be moved as long as its orientation and length stays the same.)

At this point, you may be wondering why we bother with the parallelogram method at all. The reason is simple -- it is most closely related to the component method of summing vectors, which is an important method for finding the exact length and direction of the resultant vector.