To determine the position of a particle in space, we use a position vector that starts at the origin and ends at the location where the particle is. Using the position vector, we can uniquely determine the position of an object in space. Also, the motion of a particle can be described by using the position vector precisely when the particle is changing position in time. The position vector also changes and that leads to the formation of the displacement vector which is equal to the final position minus initial position as a vector. Let's look at what happens when we have motion in two dimensions. That is, when we have motion in play. Later on, we will easily go to three dimensions. To do this, I will use some kind of trick and I think those more careful listener will figure out what it is before I discovered. Let's work in two dimensions for now. The difference between the two positions of the particle can be defined by the difference between the two position vectors. Thus, if we have the particle at one moment being in the position R1, call this position initial, at another moment in position R2, call this position final position, then we can talk about displacement in the play. Delta R is equal R2 minus R1, as it is shown right here. Remember, displacement is always equal to the final position minus initial position. Okay, now let's look at this motion in two dimensions. Let the red particle move along the path indicated by the red line. Reserve this motion of this particle between two moments. We have the initial and the final position of the particle. Of course, then we have a displacement in play. How can we describe this kind of motion? I already mentioned such a motion in one of the previous videos, but anyway, two dimensional motion can be described by two one dimensional motions. Let's repeat how. Well, each point in two dimensions is uniquely defined by the two coordinates. We can label them as we want, but it is common to use X and Y. I deliberately omit these labels from the graphics, because I think it's important that your imagination is constantly working in the learning process. So, let's put it this way. The position of the red particle is determined by two coordinates, and as particle moves, its coordinates also change. Now, let's imagine a virtual particle that moves along an axis just like the coordinates are changing. For example, let's take virtual particle to be a green one. Obviously, it is a motion on a straight line. This green particle represents changes of one coordinate of the red particle. Similarly, pink particle represents changes of another coordinate. Just a little comment. The displacement of the red particle can therefore be determined by using the displacement of the pink particle and the displacement of the green particle. When we know these two displacements, then there's some is the displacement of the red particle. Does anyone already understand the trick I mentioned? Still, let's look at some other characteristic two-dimensional motions. And, finds, if they can be described by two one-dimensional motions. For example, this one. A little more complicated than the previous one can of course be described by two one-dimensional motions. Displacement of the red particle can be determined by two displacements on the corresponding axis. Again, displacement of the red particle is the sum of two displacements at the axis. What about trick now? They're getting it. Of course, but let's look just one more motion. This one looks like a ballistic shot. Again, the motion of the red particle can be described by two one-dimensional motions. Displacement of the red particle is the sum of two displacements at the axis. Trick? Of course, now everyone figured out what is going on here. I'm actually showing to you a single three-dimensional motion. All the time we observed the motion of the same red particle. The only thing was changing is the perspective. If you told so, you were right. Actually, the true meaning of this is to show how can you describe three-dimensional motion using three one-dimensional motion. Now, let's look at these three motions at the axis. By analyzing these three motions, we can describe the observed three-dimensional motions. Can it be mathematically related? I mean, how to mathematically relate three one-dimensional motions to one three-dimensional motion? Quite simple. All we need to know is where the particle is at any given moment. So, it is a position of vector that we need to know. Precise, we need to know the dependence of the position vector on time. With this, we can determine other kinematic quantities such as displacement, distance, velocity, speed and acceleration. Obviously, the connection is this. Each position vector is expressed by its three components. So, if we want to determine displacement in space, we need to know three displacements on the observed axis. We see that the vector sum of these three displacements is equal to the displacements in space. Therefore, displacement can be represented as three consecutive displacements parallel to the axis. So, if we want to know the displacement in space, then we must know the components of the initial position vector and the components of the final position vector. It is then obvious that the displacement delta R can be expressed over three displacements delta X, delta Y and delta Z. Perhaps it is better from this point of view. Now, average velocity. Average velocity, which is defined as delta R per delta T, can be expressed by three components. Delta X per delta T, delta Y per delta T and delta Z per delta T. Of course, instantaneous speed can be expressed by its three components. The X per DT, the Y per DT and the Z per DT. I hope this video was helpful to you. Thanks for watching. What? Nobody repels. Does anybody notice a mistake? Of course, it is about instantaneous velocity, not instantaneous speed.