 So now we're going to look at a slightly different way to write out the equation for magnetic force using something called a cross product. So starting off with the equation we've already seen for the magnetic force on a charge moving through a magnetic field, we had F is equal to QVB sine theta. Where this last part of the equation was sort of our perpendicular multiplication between V and B that we looked at when we first derived this equation. Well, if we're going to use vector notation, there's actually a special way to write out this perpendicular multiplication called a vector cross product. If I write out the vector cross product using this vector notation, my force equation is going to look like this. Where now my vector force is equal to QV cross B. And this V cross B is this vector cross product between the velocity and the magnetic field. So I could say that the force is equal to the charge multiplied by the vector cross product between the velocity and the magnetic field. Note this is not just a multiplication sign. Don't say times here or just multiply. It's also not the X variable symbol either. This is a very particular symbol that represents a mathematical operation in vectors. If I were to take this equation and note that my vectors means I've got components for V and B in X, Y, and Z, then I could write out this cross product as a term by term equation using those components. And when I do that, it's actually quite a large equation here. Notice you've got your Q out front and that's multiplied by the entire thing. And then you've got these individual terms for I, J, and K, giving us the X, Y, and Z components of our force when we're all done. Because a vector cross product, unlike a vector dot product, you have a vector when you're done at the end. Now if you look carefully, you'll notice that for the X term, which is represented by I hat, I have Ys and Zs as the components that are involved here. Where I've got my J hat, which represents the Y component of the force, well I've got X and Zs here. And for my Z component of the force represented by the K hat term, that's where I've got X and Ys. So there's something in here about how each component depends on the other two components. Now another way to express this mathematically, which will make sense if you had linear algebra, is that I need to find the determinant of this matrix here, so I've got my I, Js, and Ks, and then my components in X, Y, and Z for the velocity in the magnetic field. Now if you haven't done determinants before, I'll give you some more instructions in another tutorial. But for right now, this is the other way of remembering what I'm doing when I'm doing the cross product. So that's our end of the introduction to the cross product. We'll still need additional practice to make sure you really understand what's going on.