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Polnt) Glve vector paremetrc aquation for Ihe Eine through the poirt (2, 0) that Berpendicular '0 the IineSt,4):L()...

Question

Polnt) Glve vector paremetrc aquation for Ihe Eine through the poirt (2, 0) that Berpendicular '0 the IineSt,4):L()

polnt) Glve vector paremetrc aquation for Ihe Eine through the poirt (2, 0) that Berpendicular '0 the Iine St,4): L()



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Given $\quad \mathbf{r}(t)=a \cos (\omega t) \mathbf{i}+b \sin (\omega t) \mathbf{j}, \quad$ find the binormal vector $\mathbf{B}(0)$

Question asks us to sketch a few vectors representing a specific vector field on a specific line. The first water vector field. It's F is equal to zero comma one. And so we call this a constant vector field because it doesn't have any points in there. No exes, no wise. So every point is going to get in the same and we're looking at it along the line. Why is equal to two? So let's draw our plane here. The axes. We got our X and Y axes here and then I'm going to make this line Y equals two. So we pick any point for any value of X. We're going to get that our vector. Let's say this point it. Move zero in the X direction and one in the Y direction. So it's smooth. Straight up a unit, we pick a lefty, let's say for a negative value of X. Same thing is pointing up. In fact, we're gonna go to any point we want, and we draw the same exact vector in my drawing. They may look different, but conceptually these doctors are supposed to be identical. They each point won in the Y direction and zero in the X direction. So here are representative that there's along this line

Question. RG it, Could you the new camps Agent D then d go Society and e d sancti. And from the question 115 own question 115 We have that unit tension fetter tt we could you one out of screwed up six and then we have that you Ah, go site The answer we have Young will go side they when? A side day and no course that the parasite they asked the result we got from the question 115 And now when the question asked to find the unit normal vector and D by the formal agenda Anti week agenda deep Rempt e over the No mom Dirty pre empty and were given up d print it at the unit. Sentiment is given here, and I'm so we need to find and I'm the They're here. So first of all, we need to find, uh, deeper, empty first so I can do it here. Taper empty. We get Nico Drew became the one items with six outside and some God is Oh, And now that the review? Because I could u minus sign the initial minutes. Course, I think you were gonna minus side day and bless. Go, Sandy. And then the second thing we need to find And no, I'm this one. So the new MTI plenty, and we're going to no square root off. Ah, well, bring wicked, uh, one on top scored six. You have this one square root hand, and we will have one of them's with him. Six outside, inside with him. Reserve Square Plus doesn't will be menace I d minus course I day square in place because I d minus I day square on. And if you have this one, we're echo to one out of screwed up sex outside Squared off Yeah, vision And we expend the square on the square Which again this sigh day square plus two sides The Thames course I day and bless course I square today And for this one we enter plus course I square the Manus troops. I take coarse Itay and blessed with this site square today and we think can cost out this one with this one. And follow size crab discourse has great under one something parties on the square. So totally we get will be one of them Suite of six times the square it off. The one was going to be true. So we get Nico Gender Square root off the 100 tree, so document it deeper. Empty now. Phone. Yeah. Now then you need no more Victor Anti. We're going to no one on the skirt of six zero minus. Uh, they manage score side day A man aside, Day press corps society devalued by the one of a skirt of three And we want to find and off the zero. So when we bulldoze the inside first this one signifying with this one and then we get a co two. Ah, that's squared off in Ah, uh, three. Dividing by six We're gonna wanna talk to on now. In sandwich you get will be zero good as the inside here. And then we should get this. I could Jizo course. I'm sorry. Could you one from Ghana, man is one here and here we go on the one. So around the finance, I will be one of her skirt up to and so minus 11 And that's when we don't find an answer here

Okay, so we're asked to find that unit normal vector at cuticle to Del. So what we need to do first is we have our tea. It's equal to to e Hunty e Geico side of things. An e e g sanity. You need to take a driven of abyss and then evaluated at zero. There is a motive is to be tipsy utility sign of tea by this sign of tea. And you two g close. I don't see a sign of tea. Okay, now let's take are magnetic. Okay, That gives me two entities to your team Squared plus even t co sign. Do you want a society squared? Plus our eternity co sign a T. No sign of C. You're holding squared. Okay. It's just simplifies to just scurried of six feet 60. Okay, okay. So we also have We need to find a normal vector of our hi Monty over the magnitude of our privacy. So let's do that. We get what was our priority. That was too easy to see. Unity courtside, at T minus sanity. And here the tea China tea. That's cause energy all over square roots of 60 60. This simplifies to just general common negative sanity. Negative pro sanity over screw of six and negative sanity. Cresco, Sanity all over. Screwed of six. Out. What's not the grit? So you with that scratch that that's actually just two over skirt six calm CO sanity when its sanity all over it is over. Six Finerty all over the school to six now looks like the derivative of this gives a serial comma. They go sanity minus coach entity over square root of six and they go sci fi close co sanity over a skirt of six melody Valerie, this girl, you get zero common negative one over square root of six one over square root of six. Take the magnitude of that and we get they're all plus one over six. Plus one over six. Gives me one over square root of three. Okay, Now our normal Becca evaluated that Sarah is equal to what we have here divided by our magnitude. So that's they're all common. Negative one over square root of six when I was growing of six times square root of three that simplifies to square with two over two times zero comma negative one comma one

For this question. They want you to know there is a very important on the zero vector. It's the vector given with co ordinate zero for the X coordinate Zero for the wife ordinance is equal. You would also go Sky Cordon, Jake Won and the cake order. They all have zero.


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