This was written a while ago so sorry for any errors.
If a particle is moving in a straight line, it can only go in two ways. One way to look at its action is as good, and the other way as negative. However, a plus or minus sign is no longer enough to show the direction of a particle moving in three dimensions. We need to use a vector instead. This chapter talks about the (vector) rules of combination that work for vectors, which have both direction and size. A vector variable is any number that can be shown as a vector because it has both a size and a direction. These are some examples of vector numbers in the real world: acceleration, motion, and displacement. It will help you a lot in later parts to understand how vector combinations work, because you will be seeing a lot more of them. Not every real amount has a direction that goes with it. As an example, the ideas of time, energy, mass, temperature, and pressure do not “point” in the usual sense. We use normal algebraic rules to deal with these numbers, which are called scalars. Scalars are made up of a single number and a sign, like 40°F. Moving from one place to another is the most basic type of vector number. If a vector shows a displacement, it makes sense to call it a displacement vector. (Acceleration and motion vectors work the same way.) Something goes from A to B and is said to have undergone a transfer from A to B. An arrow from A to B shows this change in position. The line shows what the vector looks like. There are three lines that go from A to B. They are all the same size and point in the same direction. In this way, they show the same change in where the particles are and describe the same vectors of movement. You can move the vector without changing its value as long as its length and direction don’t change. What the shift vector doesn’t tell us is anything about the particle’s real path. Displacement vectors don’t really show motion; they just show how the motion affects everything.