 In the last video we looked at bond dipoles and learned how to identify where the largest concentration of electron density would be in a particular bond. Most molecules are made of more than one bond, however, so we also want to know how to work out where the electron density will be greatest in an entire molecule. We're going to use a maths concept called vector addition to do this. This is also a technique that turns up frequently in physics. For instance, if you have several forces acting on an object and you want to know what the overall force is, then you do vector addition to find that out. We start by identifying individual vectors. A vector is represented by an arrow. The direction of the arrow obviously shows the direction and the length of the arrow represents the magnitude of whatever the quantity is that you're looking at. If we're talking about forces, it's the magnitude of the force. For us, the vector arrow represents a bond dipole, so the direction of the arrow shows you the direction of the dipole, which will be along the length of the bond and pointing towards the negative end, while the length of the arrow shows you the magnitude of the dipole. The larger the difference in the electronegativity of the two atoms in the bond, the larger the separation of charge, and therefore the larger the dipole. If you remember our examples from the last video, we had hydrogen fluoride, which had a very large difference in electronegativity between the two atoms. So we draw its dipole as a long arrow, and our hydrogen iodide had only a very small difference in electronegativity, so we draw its dipole arrow as a short arrow. In both cases, the arrow is pointing towards the more electronegative atoms. When we want to find out the sum of two vectors, that is, we want to find the combined effect of, say, two forces if we're in physics, or for us, two dipoles, we add them together, and we can do that graphically. If we have two vectors, we can translate the end of one vector so that it touches the end of the other. We now redraw these two vectors. We're going to keep one in the same position, and we're going to move the other one. We're not going to change its length or its direction, we're just going to change its position, and we're going to put it so that it is touching the end of the first vector. So you can see that this vector here is exactly the same as this one, if my drawing were perfect, and all I've done is shift it so that its end is touching the end of the other vector. Alright, to add these two together, all we have to do is then draw an arrow that starts at the tail end of the first vector and ends at the pointy end of the second vector. And then if this is vector A and this is vector B, then the red vector here is A plus B. There's another little diagram to show you. So all you have to do to add two vectors together is to translate them so that they are head to tail, and then draw an arrow that goes from the tail of one to the head of the other, and that vector is the sum of the first two.