 Let's start off with a little bit of a review from last time. So just as a quick reminder, when you go into the course content on Blackboard and you go into the folder, which our last one was the Introduction to Vectors on August 29th, it starts off with the textbook sections and the videos. And if there's anything that wasn't clear, you may want to go ahead and go through those things and re-watch any videos that you need to. Now I'm going to jump down here to where we had our grid vectors. I've got this one set up so that you can see the key for the problem we did last time. So again, it's got our additional pre-lecture stuff, but after lecture I actually put the keys to the problems that you did. I'm bringing up this one just because it's going to really show us some of the stuff that we want to do here. And I'm going to go ahead and make this a little bit bigger so it's easier to see on the video. So we have these grids and we have our vectors as arrows on these. This is how you graphically show a vector. And then we talked about how you would represent that in this sort of IJ notation. You're counting the boxes. So A had 1, 2, 3 boxes to the right and 1, 2, 3 boxes upward. B had 4 boxes to the left and 2 boxes upwards. Well, your right and left is going to be your I part. And if you go to the right, it's a plus I. Or like on B where you went to the left, it's a minus I and you put how many boxes. So here I went 1, 2, 3, 4 boxes to the left so it's minus 4 I hat. Same thing happens with up and down but that gives us our J hat component. So A went 1, 2, 3 boxes up. B went 2 boxes up. And if we look down here at D, it went 1, 2, 3 boxes down and 2 to the right. So it was plus 2 I hat for the 2 to the right and minus 3 J hat for the 3 went down. And remember if you've got something horizontal, that means there's no up and down and the J is going to be 0. And if you have something going vertically, that means there's no left or right and so the I would be equal to 0. So last time we did these ones where if I give you an arrow on a grid, you can figure out what the equations is. Then on the bottom part of the worksheet from last time, just again as a reminder, if I give you an equation, you should be able to draw it on a grid. So in this case we had 3 I hat plus 2 J hat. That means it should have gone 3 boxes to the right, 1, 2, 3 and 2 boxes up, 1, 2. So this one is shown with 3 I and 2 J. And on this case for B I went 1, 2 to the left and 1, 2, 3 down and etc. So this was what we did from last time. We're going to do something similar to this as sort of a first step on our problems today. And just to make things a little bit easier both for you and for me, if you look at the worksheet you got and again that should be in your pre-lecture folder for today's lecture, I also handed it out in recitation. You'll notice that we actually start with these same four vectors but then we're going to do some vector math on them. So looking back at the key for the 29th may help you out as you're trying to understand what's going on. This is also a good time to remind you that if you're in that course content for the particular day and you scroll down underneath that key, you always want to click the mark reviewed button and then that will tell me that you're actually going through and doing everything. And it's the same thing for your textbook sections, you want to go ahead and mark those off as reviewed.