For the following material it is necessary that you have a good understanding of vector addition.

Let us use Property 1 of the difference to find the difference between the two vectors and shown above. Thus, we need to find a vector, denoted - , that added to gives ,

+ ( - ) = .

To find this vector you can arrange and tail-to-tail, as in the diagram above, and then draw an arrow from the tip of to the tip of , resulting in the green vector. Convince yourself that the green vector satisfies the given equation.

This way of finding the difference vector - will be called the comparison method here. Reason: by joining the vectors tail-to-tail, we are comparing them. The separation of the two tips is a measure of how different the two vectors are. If the tips coincide, the vectors are the same and their difference is zero.

The comparison method takes advantage of Property 1 of the difference. On Page 3, the difference will be constructed using Property 2 of the difference.