Two displacements can be added together by drawing a scale diagram.

For example, if a body moves first from A to B and then from B to C, the final displacement is the same as if the body had moved directly from A to C (see diagrams below).
 

Displacement is a vector quantity. It would seem reasonable to assume that other vector quantities (for example, two forces or two velocities) can be added using a similar method. (This can easily be demonstrated for forces. See experiment 9M.) Consider these two forces:

The resultant of these two forces can be found by drawing a "triangle of forces" as shown below.

However, when we have two forces to add together, they are often acting at the same point.

For this reason, we usually draw the diagram in a slightly different way, in order to make it look more like the situation to which it applies.

First move the vector representing force 2 as shown below.

Now, complete a parallelogram.

The resultant force is represented by the diagonal of the parallelogram in between the vectors representing the two forces.

• Exercises