 Now we can look at the other formula for calculating the magnetic force on charged particles. And this one's a little more complicated, so we're going to take it in a couple of steps. But the equation here gives you the vector force on a charged particle due to a vector velocity and a vector magnetic field. And this isn't the normal multiplication, it's a vector cross-product multiplication. Now I've got another video that actually goes through the process of explaining cross-products. And for my students, I also have a reference sheet to help you out. But I want to take a minute to just explain a little bit more about how we can work with these things. So our velocity vector potentially has an i, a j, and a k. Where i goes with the x component, j goes with the y component, and k goes with the z component. And similarly, you'd have values for your magnetic field, which is going to give you an x component in the i hat direction, a y component in the j hat direction, and a z component in the k hat direction. Sometimes they're given to you symbolically like this, and you're doing a bunch of algebra to figure out the cross-product. But you also may be given it where you've got numbers in these values. And if you're lucky, they gave you the actual vector in vector notation, and you just have to follow the pattern to figure out the cross-product. Sometimes, however, they give you the information about the vectors in a little bit of a different way. So I just want to remind you a little bit about what this i, j, and k stands for. Now there's a couple different ways to depict this, so what I'm doing is one possible way that could be done. In my class, we use the x-axis as the horizontal line when you're graphing something on your paper. So towards the right is plus i hat, towards the left is minus i hat. j is the y component if you were graphing it flat on paper. And so upwards on the page, or towards the top of the page, is going to be plus j hat, and towards the bottom of the page is going to be minus j hat. Now if you've got this on your screen, it's towards the top of your screen or towards the bottom of your screen. Now we're not very good at drawing in three dimensions when we have flat paper and flat screens. So up to now in a lot of our physics, we haven't worried about the z direction. From my classes with this being the positive x to the right and this being the positive y upwards, the positive z would come out of the screen towards you. Now sometimes they'll actually draw that as a little bit of a line and try and give you like a 3D perspective that we're looking at at a little bit of an angle. And so you can imagine that's coming out towards you. But of course that could also be a vector flat on the paper between the negative x and the negative y. So we have to be a little bit careful here. So you're imagining that you're seeing this z coming straight out of the page towards you, which I can't do on the screen very well. Similarly the negative z direction would be going into the screen. And again sometimes they'll draw that as a little line back here that you can imagine going behind the screen. But that can be very deceptive as well. So we use the right, left, up, down, and then out of the page and into the page for our z directions. Now sometimes you're given information about the vectors such that you actually know something about them going towards the left or the right, or up or down. Now I'm particularly giving my students some hints here for my class and the practice problem that they have to do today. Where they have a velocity of a particle going towards the right, and then they have a different piece of information that tells them they have a magnetic field which is going up towards the top of the page. And so they would be able to turn those into vectors by recognizing that this red arrow for the velocity is towards the right, meaning it's in the positive i hat direction with no up or down and no in or out. And so they could express that velocity then as a vector where you've got the speed in the i hat direction zero in J and zero in K. And that represents my velocity here. Let me use the same colors just so it's clear. And then my magnetic field which is directed towards the top of the page. Again, I'll make my colors consistent here. Is in the positive J hat direction with nothing left or right, so you've got zero i hat, and again nothing in the page or out of the page, so you've got zero K hat. If it had given me different descriptions in terms of things going left, right, up or down, I would want to adjust that as well so that if it told me it was up or down, that's J. If it tells me it's left or right, that's I. And if it tells me it's into the page or out of the page, that's going to be your K hat. Once you have your vector in vector notation, either because they gave it to you, or because you've read the verbal description and translated it into vector notation, you're ready to actually start the cross product. And I'm going to do that in a separate video.