>> Product. Before we start the manipulation in making the calculation of cross product, I wanna talk to you a little bit the nature of the result of cross product. I have in my hand a few vectors here. Now, we know that vectors have characteristics of magnitude and direction. The magnitude of each of these corresponds with their link. Okay, so that's no big deal. So, direction though, now if I take the direction of these two and I configure them like this and let me twist my entire coordinate plane a little bit and show you want I'm doing. You see these are kinda off kilter from one another. But you know when I'm talking about vectors I can move vectors around. As long as I don't change the direction of these vectors I can move them like this and like this and so forth. I really am talking about the same vector, am I not? Alright, so I can actually then put their initial points together like this. And I can then by that method realize that any two vectors sort of define a plane, that is, a plane contains any two vectors, and I can show you the plane. I can take my entire three-dimensional coordinate system and I can twist it like this. And now, we see that it's contained within this plane. Alright, that's one idea. Now, once the calculation is made for cross product, we are calculating a third vector, a third vector, and that third vector turns out to be orthogonal to the first 2 and orthogonal to the plane containing them. That is, all right I'm again twisting our entire coordinate plane. And now here's the plane containing the vectors and the cross product will give us a vector which is orthogonal to these two and orthogonal to the plane containing them. And actually there are a couple of ways of calculating cross product. We're gonna look at a U vector and a V vector and we're gonna calculate U cross V. And then we're gonna calculate the V cross U and it will turn out that one of those will be a vector on this side of the plane, orthogonal, and the other will be a vector on this side of the plane also orthogonal.