The parallelogram method of adding vectors is easier to visualize when we add two vectors that are acting at the same time.

Two ropes and the forces they transmit.In this image, two ropes are attached to an object (not shown).  Which way would the object most likely move?

If you said in a direction somewhere between the two ropes, you would be right.

Applying the Parallelogram Method

To use the parallelogram method, first draw the two vectors.  In my example, we will call them \(\color{black}{\vec{A}}\) and \(\color{black}{\vec{B}}\).  You should draw them to scale, using a ruler and a protractor to get the lengths and angles correct.

This animated .gif shows the method described below.

Animated gif of the parallelogram method
You then draw a parallel line across from the first vector, starting at the tip of the second vector.  I usually draw this as a dashed line, since it is not an extra vector.

Next, draw a parallel line across from the second vector, starting at the tip of the first vector.  If you have drawn things carefully, the original vectors and the two new sides will form a parallelogram.

Finally, draw a straight line from the tails of the two vectors across the diagonal of the parallelogram.  Add a pointy end to the line where the two new sides meet.  You have just drawn the resulting vector,

\(\color{black}{\vec{A} + \vec{B} = \vec{C} }\).