 In this video, we're going to take everything that we learned from our previous videos on vectors. Whether we're converting from polar to rectangular or rectangular to polar, we're going to be doing all in this addition of vectors. So in this video, I've got, let's move that right on back. In this video, I have three vectors. I've got one vector here, 20 volts. I've got this vector here, 35 volts, and I have this vector here at 100 volts. Now, we need to look at these. We're going to use this 20 volts as our reference. I'm going to say that this guy here is 20 volts and zero degrees. I've got 35 degree angle in here. So this will be 35 volts at 35 degrees. And then beyond that, I have 100 degrees. So I'm going to add that 100 to the 35. So I'm going to say I've got 100 volts at 135 degrees. Now, the first thing we want to do when adding any vectors is we want to put up our x, y chart. So I've got myself an x, y chart up here because it gives me a reference. Then I start figuring out what my rectangular version of these polar forms are. So I'm going to take 20. I've got 20 at zero. It is all x. So I've got 20x and zero for the y. So we're going to get that plugged in here. Now, for this guy here, I've got 35 volts at 35 degrees. So what I'm going to do with that is I'm going to take the cos of 35 degrees times 35 volts and I get my x, and I'm going to take the sine of 35 degrees and multiply that by 35 volts to get my y. And that gives me 28.6 on my x and j20.1 on my y. And my last one here is just going to take the cos of 135 degrees times 100 volts will give me my x and the sine of 135 degrees times 100 volts gives me my y. So plugging that into the calculator, I get my x being negative 70.7 and I get my y being 70.7 as well except it's negative 70.7 here because we can see that if I drew this into a quadrant system, this vector here is in my second quadrant. So it would be a negative x and a positive y. Now I go ahead and I add up all my x's and I add up all my y's and I get my rectangular version of the addition of these vectors. So I get negative 22.1 for my x and j90.8 for my y. Now I've got a bunch of numbers here. What I'm going to do and I would suggest you do this if you're working on these is draw up a separate quadrant just for this vector alone because you're just going to end up getting yourself messed up if you start trying to add it to this bunch here. So we're going to do that right now. So here we go. I've got negative 22.1 here. That moves me into the second quadrant and I've got j90.8 here. Then I'm going to work out what my resultant is. So what is this guy here? That will be the answer for my polar form. My resultant is 93.5. And the next thing I've got to do is work out what my angle is in here. So we're just going to go negative 22 or just take 22.1 divided by 93.5 inverse cos that and I get an answer of 76.3 degrees. Now again, we are in quadrant number two. So my answer is not 93.5 at 76.3 degrees. I've got to take 180 degrees here and subtract 76.3 degrees from it. So 180 minus 76.3 gives me 103.7 degrees. So taking those three vectors and adding them together, I get an overall resultant of 93.5 at an angle of 103.7 degrees. And there you go. So all you have to do is if you didn't really follow through with this one, make sure you go back through the other videos, go over how to convert from polar to rectangular, rectangular to polar to the quadrant system. It all comes to a head in this one here and we have ourselves vector addition. And it doesn't matter if I have one vector, two vectors, three vectors, I just keep putting the x and the y's in and then add them up all in the end.