5

Iet 0lt) =cost,1 sint,cst) Then the normal vector of & i8 equal t2) N() =cos t, Sin &; COSb) Nt) =cos t , sin ( costcost,sin/ ,costAnswer &0Answer b)@&#...

Question

Iet 0lt) =cost,1 sint,cst) Then the normal vector of & i8 equal t2) N() =cos t, Sin &; COSb) Nt) =cos t , sin ( costcost,sin/ ,costAnswer &0Answer b)@'NQ) =

Iet 0lt) = cost,1 sint, cst) Then the normal vector of & i8 equal t 2) N() = cos t, Sin &; COS b) Nt) = cos t , sin ( cost cost,sin/ , cost Answer &0 Answer b)@' NQ) =



Answers

\begin{equation}\begin{array}{l}{\text { Find the normal vector } \mathbf{N}(t) \text { to } \mathbf{r}(t)=\langle 4, \sin 2 t, \cos 2 t\rangle}. \end{array}\end{equation}

The girls are nt you could you do society five day and you go side day And the question asked us, Joe, find ah unit normal Better empty which is defined as that day brand d even you might a number t prank t Well, uh, the deep rem day. We just, uh, that the primitive unit tension But the ICO June hombre empty, even Imagine number are, um the yeah, So let's try to find the unit tension with their first. So we need to find first thing will be the are empty Can you go do what you do the river, the inside here and then we get a go jin that you go society five and two Manus to society and then the No Mamdouh Bronte and we're equal juice squared off and we square this every single component and with some of your mom which get any coaching the phone cause I square day plus 25 plus force, I squint. They notice that this one would is when we're gonna go too far, then from again discouraged for plus 25 coach you the square root of 29. And as a result, we can unit tension went you called you one out of skirted 29 Teoh, go side D five months, two side day And now to find a no under no done unit, no more. Better When did you find a day per empty? So I get good you want ever scored 29 We don't really do And then we get good humanist you sci fi zero and man has to go society And then the nonentity primp d again you're going to We will have This one is a constant were given outside Inside we have a square root off Uh uh huh This one square and then we're gonna force I square day Plus there are plus for course I square day that it doesn t Could you fall on? Therefore we get exactly Go do the square root off the value by square of the 29 So he could you do undiscovered on 29 the final answer would be then no more unit normal that we could you this one over this So we get now we'll be one of up skirt 29 when its two sides day there are honest too. Go side day and now dividing buying a Jew all over square under 29. Here we can consider the scorer that deny here and then we have left with the one out of two Onda. We can cancel a Joe here as well now in the final. And so will be minus side. They though, and, um, miners. Course I today. That would be fine. Answer funded unit. No more better 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

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

1 7. This question will be learning about the basic concept of the vectors and the scala's. The question is let Director given by I get a cost to the let's Jacob a sign data be any better. And another vector which is B. And it is normal to a better so that know the better be would be given by Out of the four options. Like so for normal vectors we know that the dot product of two vectors is judo. So erected would be well to would be equal to zero. Yeah. So this is the case with the director which is given in the option seat. Yeah. So we can check that a vector is I kept a constant to let's Jacob sign data. Dog. The big factor is I kept the same data minus Jacob because data ask anyone in the option C. Right? So when you simplify this, we get every scientist Bastida minus every scientist to cost data Which is equal to zero. Now, since the dot product is equal to zero, it means that a director and be record perpendicular to each other. Right? So therefore the Director was just given the option. C. Is correct. So be rector would be will do I kept the scientist to minus Jacob because tita. Mhm. And the correct option is the option C.


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