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Compute the unit normal vector N(t) forr(t) = (sin t, 2t, cos t)...

Question

Compute the unit normal vector N(t) forr(t) = (sin t, 2t, cos t)

Compute the unit normal vector N(t) forr(t) = (sin t, 2t, cos t)



Answers

Find the unit normal vector $\mathbf{N}(t) \quad$ for $\mathbf{r}(t)=\langle 2 \sin t, 5 t, 2 \cos t\rangle$

In this question Here we record that we have the unit tension with T Smarty, you go to the, um property. Do you have any by the are from t taking the norm here something we can have a normal better nt He coaching attention with prime If anyone didn't know on attention for the prime and now a discussion were given the vector function anti you go to the fourth sign after duty goes on and on the 2. 30 The first thing to compute a tension vector here we need to find our property. Then we get ICO too. Zero this one in Continue to course I do t just getting to to manage to side duty And then we can find a normal the arm from t get equal to the square it off Here we have does their square plus the farm cause a scratch your tip plus mhm side square duty. So it was unified Here you get to go to the square it on the farm on going to the to and they're far from here. They confined a tension victor it would go to Yeah, zero here and then course I do t and then the manners. Sad duty. And from here we can find a number victor. Now, first we need to find a deep ram t It was equal to zero. You're going to manage to side duty. They shouldn't get a Manus to, because I do t And then then no one with the prime t let me go to the square root off. There's gram plus so so square to t plus four courses squared to D, which is equal to the square it off the mhm which is able to to as a result, here you can get a normal vector. Anti ico tube, the zero here minus I duty my enough first time duty and this could be the normal vector we're looking for.

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

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

I guess we are. G is equal to to your sanity, Grady. Inside of tea to 70. Okay, we need to find our unit 10 directory. So take note of of Artie, That gives me negatives to sign of tea. Three and two costs energy. Now, let's take the magnitude of our primacy that gives me describe it of 13. So our attendants Bechler into culture. They have to sign of cheap gray and to co sign up, see all over Mrs Corbett of 13. Okay, now we're asked to find that units normal vector. So we need Thio. Take derivative of T. That gives me need to over 13. Garrett of 13. Co sign of tea. Sterile and negative to overdo Gene spirit of 13. Sign it. E No, we need to take the magnitude of that. Okay. Square roots of this holding squared. Plus, that morning squared that simplifies to this to screw whatever Tune over the Tyne for a normal rector. Know what unit vector is equal to? Um, what do you say I gotta to over 13 square bit of 13. Cool sanity. Zero and two over 13. Screw it. 13 sanity all over to scare a little 13 over the city and that simplifies to anarchy is equal to negative coastline of tea zero and negative side of T. Okay, now we're asked to find our final affected, but I've I know by normal, by normal I know that there is B a t is the cross product that tea cross and so across them we get This is it's a negative to over 13 screw. It's 13 sci fi. They're all oh, you know, three square with the other team trumpeting and two over the team spirit of 13 cool side of t crossed with negative coastline of tea They're all in the society. You take the cross product of these two. You see that this is equal to I got a three over 13 square root of 13 sign that negative to overthrow its energy and over the Tyne and three over 13 square root of 13 cool society


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