Dot Product of Two Vectors

Let's talk about the dot product of two vectors. We have two vectors like this: F of x, x direction, y direction, z direction, so on and so forth, right? So how am I going to find dot product? There are two methods. The method one is this: F of x times G of x, just simply multiply as, say, product, right? F of y times G of y, F of z times G of z, and then you sum them up. Let me write this; I'll be right back. Okay, here you go. You can see over here. The second way is also to look at it this way: this is the amplitude or the magnitude of these two vectors, right? And then multiply by cosine of the angle between them. Theta is 0; cosine 0 becomes one, so basically multiplication of these two. If theta is 180, this becomes a minus one. If it is 90, cosine of theta becomes zero, so this goes away—it becomes zero. How do I obtain these? Let me write that, and I'll be right back. Alright, here you go. So you can see, F of x square, F of y square, F of z square, square root of it, and the same thing for the other vector as well.