This method has
advantages in being easy to apply, especially when multiple vectors are to be summed.
To sum vectors using this method, simply move them such that the head of one vector
is attached to the tail of the other. Once all the vectors have been "chained
together," the resultant vector is easy to discern  it is simply a vector that
points from the start of the chain to the end. The following applet demonstrates
this method very well for any two vectors.

Can we really move vectors around like that? What are the rules for
moving vectors? 
Applet by B. Surendranath Reddy
Using the mouse, create two vectors. Notice that when moving a
vector its length and direction do not change. Notice what happens when the tail of
one vector is placed on the head of another  the resultant vector appears. Note
that this resultant vector points from the tail of the first vector to the head of the
second, just as we described earlier.
Notice that the parallelogram method shares the same basic
disadvantage as the headtotail method  finding the exact length and direction of the
resultant vector is going to again require some sophisticated trigonometry.
Therefore, this method is also used mainly to provide a general, qualitative
description of the sum of one or more vectors. 