Adding vectors using the tip to tail method is fairly simple.  In fact, in the previous lesson, we did just that.

We have been representing vectors using arrows.  The beginning of the arrow is often called the tail of the vector.  The pointy end of the vector is referred to as the tip of the vector.  If an arrow was in flight, the tip of the vector leads, and the tail of the vector follows behind.

Using the Tip to Tail Method

Essentially, you draw the first vector, typically starting at the origin.  You then draw the second vector, starting at the tip of the first vector.  Finally, draw a line connecting the tail of the first vector to the tip of the second vector.

This animated .gif shows the steps described below.

Animated gif off tip to tail method

Two vectors added together.In the diagram, we draw vector \(\color{black}{\vec{A}}\), then \(\color{black}{\vec{B}}\).  To determine the sum of the two vectors, we draw a straight line that starts at the tail of \(\color{black}{\vec{A}}\), and ends at the tip of \(\color{black}{\vec{B}}\).

If we call the sum of these two vectors \(\color{black}{\vec{C}}\), then we could write \(\color{black}{\vec{A} + \vec{B} = \vec{C}}\).

We can easily visualize the tip to tail method with displacement vectors.  We start at the beginning, then move along vector \(\color{black}{\vec{A}}\).  Once we reach the end of this first vector, we move along vector \(\color{black}{\vec{B}}\) to end up at our destination.  Alternatively, we could have taken a shortcut, following along the path marked by vector \(\color{black}{\vec{C}}\).