Intelligence? Um. There is a homework assignment associated with this that will be due in two days, and I will be giving you that shortly. I will give you the assignment, handle it as you want. So. So. So. So. So-so-so-so-so-so. Um. So. Don't start with the today, tomorrow Friday. Yeah, Friday's the first. So the homework is not due until next month. Good point. No. Find the vector in component form and find what its magnitude is when the point is (-7,4) and the terminal point is (5,-11). Cray-on. Can you say crayon? Wait, I don't want that number. Crayon. It's still terrible. Find its magnitude and initial oh wait. Find the vector in component form and its magnitude if if its initial point is (-7,4) and its terminal point is (5,-1). Now. When we say a vector is. Let's go back. When we say a vector is, let's say <1,-4>, that means that the vector starts at the origin and the tip is at 1 and 4 over, and so you have to slide it over so that it is at the origin. So this particular vector, you're going to see the shortcut here, -7 4 and here's its initial point, then 5 negative 1, there's the terminal point, so the vector looks like this. -7,4 and this is 5, -1. I want to slide that vector over. Take this. Tear something that has the length of that vector. Hopefully possible I am going to make a little vector, slide the vector, this is technology at work. So. There's that vector. I don't know. Okay. Thank you. So. Here's my vector. Well, remember. Vectors are equal if. What two conditions have to be met for a vector to be equal? Length and direction. I am not going to change the length and direction, or slope and direction of that vector, but I want to start at the origin so I am going to slide it so that it's just right here. So my question is that to find the component form, so basically I need to find the coordinates right there. You just find 12, -5. All you did is you took your terminal minus your initial point because basically you want to slide it over 7 to the right so that the x-value is zero, so we're doing the opposite of the x, and then we want to slide it down four so that it gets to the origin (over seven, down four) and so what we're really doing is your terminal minus your initial to get your i and j. Your vector, our vector, in component form is going to be <5- -7, -1-4> which we were told is 12, -5. The component form means that you are showing the two individual components. Or the vector equals 12i - 5j. Component form means that you are showing the distinct directions, the horizontal and the vertical. As far as the magnitude, that's up to you to figure out, and that shouldn't require a calculator if you knew your pythagorean triples. 12 5 144 25 169 so 13. Everybody has the opportunity to turn in assignments early. Depending on your schedule, it's time management. Oh my gosh, that's the homework. Wow. I didn't mean to give you that. That. Sketch each ... what? Well. I don't like the directions. It says sketch each scalar multiple, and all I want you to do is find the components of the vector. They give you a v. We'll do an example, we'll right the book examples, and then I'll show you what I really want you to do. Example 2. What we're going to do is. It says. Can you remember what's going on here? In paranthesis is what the book is asking you to do. (Sketch each scalar multiple of vector v). What we're going to do is they give you a vector alright sketch each scalar multiple of v. Yes. Two v negative 3 v, so they're asking you to do these (a) 2v, (b) -3v, (c) 7/2 v. Put it into the form so that it is. All that I'm looking for is what would be 2 times vector v -- well, 4 6. Just covering our bases but some of this is pretty darn simple. So what they would have wanted you to do is draw vector 2 3 and then vector 4 6. There's 2 3 and then there's 4 6 which is just going to be twice as long. I don't see the point. We do not have to sketch it on #18. You could write this as 4i + 6j. You'll see me bounce back and forth just to make sure you understand that it's all the same. You could just put negative Shevrons on the rank of the military and on the Shevron gas signs. I don't think so. I think this is just convenient. I roof was the video. Didn't they use the little? In the book. We always wrote them, just never called them. True. So. That's all. I just picked some problems. Because like I said, it's pretty darn straight forward. You don't have to put the or, you don't have to put versions. Oh, we should finish the last one. What would the last one be? 7i plus 21/2 j. Okay. 21 halves? Idiots are allowed to go to restuarants two (several = 2 according to Avery's customers). How many is several? Two? Oh. Yes. Let's move right along. Baby steps, baby steps. Nothing. Baby stuff, baby stuff, find vector v where u is this where would this be two, illustrate the operation geometrically you don't have to do that. There are only a few that you have to actually graph. U and w are, they are define vector u as 2,4, and then you're just adding two vectors together. Oh. Okay. Alright, so far you should know what a unit vector is. What is a unit vector? A vector that has length or magnitude of one, it's like the unit circle back in pre-cal, a radius of one. So let's try a box. Unit vector in the direction of vector v. Does the circumference of Katie's mouth change each day? Katie, your example didn't make much sense and really I am just going to move on. Yeah. I'm just going to say. Yeah. It's sort of like the cliche, someone has a big mouth. You know there's a song like that, you've got a big mouth. It's not about short people though. Hey. Maybe I can go ahead and burn these on the disc, if the van we get has a disc player, we can listen to Short People and Have a Big Mouth, a shout out for Bryan if we can find something. Alright. Unit vector means a length of one. Any old vector might not have a length of one. But if you divide it by its length, it will have a length of one. So, the vector u would be a unit vector if you take any vector and divide it by its own magnitude its own length and then you will have a unit vector, a vector of length one. Now, another way you could write this is just talking about multiplying by the reciprocal, but that's a given. What if it's a negative vector? A unit vector could be a negative - yeah, the coefficient. So that vector could be -3 i minus, so that negative is telling you direction, like down left right. So you will have some questions that ask, Find the unit vector, well we will do some, and they ask you to find the unit vector in the same direction. If you know what they are saying, you will know how simple it is. And has length one and same direction as v. So an example. Example. Example, I don't know, number one? Three? Thank you. Oh, that's true. Find the unit vector in the direction of vector u where u is defined as -3i + 4j. Oh. We're on that. That's right. It's a celebration day. I made it through another advisory. This one was an easy one. The abnoxious people were taking ASSET. So I had 7 people. Sue and Mary, and Sue confided that she had a crush on Joe Miguel, Marcos, and they asked why do they all have to be Hispanic and they had a good point and I said I don't know. We had a sub who was fresh out of college, and after you get accepted, and she was just getting her stuff in, and once you start to go to classes, you have to actually go. Getting in is the hardest part, blah blah blah, if you can afford it you can get a degree it's just how many times do you have to go through the class? Find the unit vector w. So that way we can say our answer is w equals. That's a 3 4 5 triangle so the magnitude is 5, and we are using the reciprocal, and then we have the original -3i + 4j and then we do that by (1/5) and that's what we get. If you sign up, you're obliging to the rules. If you let an underclassman out score you, you have to bring them cookies. Cookie rules. We have Dylan. If Dylan out scores you in math, yes you should bring cookies. We're not pulling the Patch thing, the Thailand entrance exams and he might be up on a few tricks, Petch can't go, he's in band and band has his solos, I've seen this kid once, is he a citizen? He's a foreign exchange. What state is the Grand Canyon in? Arizona. He doesn't comprehend that other people just don't know some things. pg 769 #2,4,9-14,24-44