5

Consider the vectors 𝑟⃗ = (3, −1), 𝑠⃗ = 4𝑖⃗, 𝑡⃗ = −𝑖⃗− 2𝑗⃗,...

Question

Consider the vectors 𝑟⃗ = (3, −1), 𝑠⃗ = 4𝑖⃗, 𝑡⃗ = −𝑖⃗− 2𝑗⃗, 𝑢⃗⃗= (−3,6), 𝑣⃗ = (−5,0), 𝑤⃗⃗ = (0,1).a) Represent the following vectors, calculate their module andtheir angle with respect to the OX axis.b) Carry out the operations:i. 𝑟⃗ + 𝑠⃗ii. 𝑡⃗ - 𝑢⃗⃗iii. 5𝑡⃗ 𝑢⃗⃗

Consider the vectors 𝑟⃗ = (3, −1), 𝑠⃗ = 4𝑖⃗, 𝑡⃗ = −𝑖⃗− 2𝑗⃗, 𝑢⃗⃗ = (−3,6), 𝑣⃗ = (−5,0), 𝑤⃗⃗ = (0,1). a) Represent the following vectors, calculate their module and their angle with respect to the OX axis. b) Carry out the operations: i. 𝑟⃗ + 𝑠⃗ ii. 𝑡⃗ - 𝑢⃗⃗ iii. 5𝑡⃗ 𝑢⃗⃗



Answers

Compute the angle between the vectors. $\mathbf{a}=3 \mathbf{i}-2 \mathbf{j}, \mathbf{b}=\mathbf{i}+\mathbf{j}$

Okay for this problem. First we're gonna decorate minus three A. That should be minus ni and minor three, right. Just one pie in minus three on a And then we want to find the magnitude and, uh ah, direction angle. Right. So here we can find the magnitude. Should be using the formula in your book. 81 last night. Which of the three times For 10. Right. Okay. And we can draw the graph for the vector minus three minus three. Something like this. Right here's Ni and here the three. So we can compute this vector. We can compare this arbor here. Our riser. Acute angle. So just arc attendant one or three. It's a the 18 point orders ring, 18.4 degree. So if you want to calculate the this angle here, the greater angle that he's a direction angle right? So start this to be cedar, then see, that should be are far plus 180 degree, which is 198.4 degree. So that is our direction angle And here's our not going to

So we have three vectors. We have a, B and C. We need to find the X and my components of each of these vectors. So we have a sub x and this is going to equal forty four co sign of twenty eight degrees. This is equaling thirty eight point eight five and we have a sub. Why, this is going to be forty four sign of twenty eight degrees and this will be equal to twenty point six six. We have beasts of X. This is equaling negative twenty six point five co sign of fifty six degrees and this is equally negative. Fourteen point eight two and then we have beasts of why this is again equaling twenty six point five sign of fifty six degrees. And this is giving us twenty one point nine seven. We have cease of X is giving us thirty one coast son of two hundred and seventy degrees coastline of two hundred seventy degrees. Is there out? So this will be zero and then see some Why, Ah, if the ex component zero that means that the entire magnitude is in the white direction, so cease of why would be equal to thirty one sign of two. Seventy. And of course, this is equaling negative thirty one. All of it is in the negative wide directions. So we can say that for party, we have to find the components of a plus B close to see and me to find X and a plus B plus c. Why? And here we have thirty eight point eight five, um, minus fourteen point eight two. And this is giving us twenty four point zero three and then for why we have twenty point six six plus twenty one point nine seven minus thirty one, and this is giving us eleven point six three. To find part B, Part B would find the magnitude and the angle s We have the magnitude of a vector plus vector. Be prospector, See? And this is give. This is simply the some of the squares of the ex component in the white component. And then you take the ah half power of the entire expression. So he would be twenty four point zero three squared, plus eleven point sixty three squared and then one half power for the entire thing. And this is equaling approximately twenty six point seven. So this would be the magnitude of that vector and then for the angle we have Ark Tan Tangent is going to be the opposite over the adjacent, which means that we're taking the Y component divided by the ex component. So the art ten of eleven point six three, divided by twenty four point zero three. And this is giving us twenty five point eight degrees above the horizontal. And that is the end of the solution. Thank you for watching.

Okay for this problem we're going to find minus a plus B. So just you that just just compute right minus a final three. Why does one and plus minus one so over to right? Happy. So just modify or what have each couple. So just add a lot minus four on a, uh Right. So for the back into, we can just use for me. I asked 16 plus one force, right, A squared plus B square and squirt. So just 16 plus, that should be, Ah, four point 03 That is actually Ah, squirt 65/2. Hey, you can just write this answer and don't use this approximately Announcer So I think right. Scored 65/2. That's enough. Hey, that's fine. The broth for this. So minus war one should be something like this. Here is one. Have and here's for so we can calculate for this angle here. That is to the our for our first should be arc attendance are contingent 1/2. Divided by 41 or eight. Right? So what else? There should be seven point one degree. Okay, so this weighs very small. So we can we can use this. This is Sabra Sita. And did this angle here should be our direction angle. So stay. There should be 180 minus. This are for which is why 170 two point. I agree, okay?

Okay for this for this problem. We're going to find you, Percy. So the plus a should just be using my instill past three. So we have a one and three plus one, which is before you so we can calculate the A magnitude by using the formula. Want us 16 a squared plus B squared because we have to come in in form here. So that's just squirt 17. You can just use arc attendant, so separate the director angle. So saying that should be our attention for guarded by one which is also for so to the 76 point there are degree. Okay, why can't we use this? Our continued directly because most of them are positive. So if you draw a graph, it should be like this. It should be like this. So here that this and go is a cute, so we can just use formula active.


Similar Solved Questions

2 answers
Use Ua standard normal tatl lo frd Ima / srrre Ihasl Loxrrosprds Ihc cuhlaty nicu Hnn Hled tp eniries, Use Ihu z-score halttuy befwet (he conesuding zHOA S Clikbvrn dnneurdard nonnnlahl Cloilum #MMa In Etllyd nadlLible (Typo = ludur D Ormetonde Ioy Occrnal uace: IudEIt ctralaImneKrER ie&anelnDrbaml
Use Ua standard normal tatl lo frd Ima / srrre Ihasl Loxrrosprds Ihc cuhlaty nicu Hnn Hled tp eniries, Use Ihu z-score halttuy befwet (he conesuding zHOA S Clikbvrn dnneurdard nonnnlahl Cloilum #MMa In Etllyd nadlLible (Typo = ludur D Ormetonde Ioy Occrnal uace: Iud EIt ctrala ImneKrER ie&a neln...
5 answers
Standard form of complex number z = (+2+302 is7-139 + [98-]16 9-19i 17
Standard form of complex number z = (+2+302 is 7-13 9 + [9 8-] 16 9-19i 17...
5 answers
Find an equation for the line tangent to the curve at the point defined by the given value of &8) x = sin t y = 9 sin & t = 3 Aye9x+ B)y = 9x - 91/3Cy=-9x+ 9-/D)y = 9x
Find an equation for the line tangent to the curve at the point defined by the given value of & 8) x = sin t y = 9 sin & t = 3 Aye9x+ B)y = 9x - 91/3 Cy=-9x+ 9-/ D)y = 9x...
5 answers
Lao LeaTEDa BotD Cumpen ethAforgthaEtokhJl Dde{FLL7MLattoI td(AuurtDelnoaTetrtetar $ [gil(AounaH2=Ann[atarateliatcudeldCattne4oromtHleftnla betatudlrar41MaltaEueal? Thald FeaTOJhporat IltdedcoDomomrd KiaheaoctentoenCaleneeAutIa {~rintn loenrrneuutudtuotetEnet UnnnDoratrui Otatit Trnti 0 I0erdeetlrt @ torrntmd ReretH Teneeureern ereenceulutu = 0 J0ldecaudeu r [Cadaeittcenadn Dau
Lao Lea TEDa BotD Cumpen eth Aforgtha Etokh Jl Dde {FLL7M LattoI td (Auurt Delnoa Tetrtetar $ [gil (Aouna H2= Ann [atarateliat cudeld Catt ne 4oromt Hleftn la betatudlrar41 Malta Eueal? Thald FeaTO Jhporat Ilt dedco Domomrd Kiahe aoctentoen Calenee AutIa { ~rintn loenrrneuutudtuotet Enet Unnn Dorat...
5 answers
Standard Normal Distribution Table Ipage 21himtidatu aimiohi
Standard Normal Distribution Table Ipage 21 himtidatu aimiohi...
5 answers
[Intthe test 0r vitellne solation irom eggyolk; Graves, Stralner paper and measure) agricultural values; egg yalk + Measuring scale 2.82 grams, Strainer paper 6.786 grams; (Egg yolk measure) = 8.72 grams: Then sal-? The Ng exit is measured after mold treatment and filtration (vitelline [iter paper) # 11,786%ramsCalculate the%o ofvitelling in GR8volk basedon hese results:
[Intthe test 0r vitellne solation irom eggyolk; Graves, Stralner paper and measure) agricultural values; egg yalk + Measuring scale 2.82 grams, Strainer paper 6.786 grams; (Egg yolk measure) = 8.72 grams: Then sal-? The Ng exit is measured after mold treatment and filtration (vitelline [iter paper) ...
5 answers
Sketch the graph of $f(x)=2^{x}$. Then refer to it and use the techniques of Chapter 2 to graph each function as defined. See Example 3.$$f(x)=-2^{x+2}$$
Sketch the graph of $f(x)=2^{x}$. Then refer to it and use the techniques of Chapter 2 to graph each function as defined. See Example 3. $$f(x)=-2^{x+2}$$...
5 answers
If $y$ varies directly as $x$ and $y=5$ when $x=2,$ find $y$ when $x=6$
If $y$ varies directly as $x$ and $y=5$ when $x=2,$ find $y$ when $x=6$...
1 answers
(II) A 32 -cm-diameter conducting sphere is charged to 680 $\mathrm{V}$ relative to $V=0$ at $r=\infty .(a)$ What is the surface charge density $\sigma ?(b)$ At what distance will the potential due to the sphere be only 25 $\mathrm{V}$?
(II) A 32 -cm-diameter conducting sphere is charged to 680 $\mathrm{V}$ relative to $V=0$ at $r=\infty .(a)$ What is the surface charge density $\sigma ?(b)$ At what distance will the potential due to the sphere be only 25 $\mathrm{V}$?...
5 answers
Solve y" | Sy' | 16y
Solve y" | Sy' | 16y...
5 answers
Use algebraic procedures to find the exact solution solutions of the equation_ (Enter your answers 35 comma-separated list: there eln(< _solution_ enter NO SOLUTION;)Need Help?AenaClnctSubmit Answer
Use algebraic procedures to find the exact solution solutions of the equation_ (Enter your answers 35 comma-separated list: there eln(< _ solution_ enter NO SOLUTION;) Need Help? Aena Clnct Submit Answer...
5 answers
Instructions: Answer the following questions using the followinginformation: ∆Hfus=6.02 kJ/mol; ∆Hvap= 40.7 kJ/mol; specific heatof water is 4.184 J/g∙˚C; specific heat of ice is 2.06 J/g∙˚C;specific heat of water vapor is 2.03 J/g∙˚C.1. How much heat is required to vaporize 30 g of water at100˚C?
Instructions: Answer the following questions using the following information: ∆Hfus=6.02 kJ/mol; ∆Hvap= 40.7 kJ/mol; specific heat of water is 4.184 J/g∙˚C; specific heat of ice is 2.06 J/g∙˚C; specific heat of water vapor is 2.03 J/g∙˚C. 1. How much heat is re...
5 answers
An automatic garden sprayer produces water spray to a distance of 1.8 meters through a angle 0. which may be varied If water sprayed from the garden spray covers an area of 2.5 square melcrs: What angle is sct on the automalic spray. in radians? Calculate the angle in degreesThe windshield wiper of a car is 24 inches long: The arca of the car glass it wipes is 600 square inches Finda) The angle covered by the wiper:b) The length of the arc?
An automatic garden sprayer produces water spray to a distance of 1.8 meters through a angle 0. which may be varied If water sprayed from the garden spray covers an area of 2.5 square melcrs: What angle is sct on the automalic spray. in radians? Calculate the angle in degrees The windshield wiper of...
5 answers
T3-EOY-MATGI-146.05Cnoose te correctansiVciCompute h'(1) for h(x) = g(f(x)) , where f (1) = 4, 9'(4) = 2 ,f'(1) = 440r3al
T3-EOY-MATGI-1 46.05 Cnoose te correctansiVci Compute h'(1) for h(x) = g(f(x)) , where f (1) = 4, 9'(4) = 2 ,f'(1) = 4 40r 3al...
5 answers
Hz Points]DETAILSMynoiesASK Your TEACHERPRACTICE ANOTHERaujecl ah ecogBLOO @Moving Jne nohc & 14 0 eug whcn avonaren dbicc # Il Inc colls 3r Hase cetetr ne thc speed @l each objcct atter the collision .Mas; 0 25moviriotnc sme dureciondlotaB.C0-g oblec
Hz Points] DETAILS Mynoies ASK Your TEACHER PRACTICE ANOTHER aujecl ah ecog BLOO @ Moving Jne nohc & 14 0 eug whcn avonaren dbicc # Il Inc colls 3r Hase cetetr ne thc speed @l each objcct atter the collision . Mas; 0 25 movirio tnc sme durecion dlota B.C0-g oblec...
5 answers
Dciariine the proportion af data that shaded urder this norrnal densily curvestundurd devlatlons_
Dciariine the proportion af data that shaded urder this norrnal densily curve stundurd devlatlons_...
5 answers
00.0 2 0.294 10.279 0.254 0.236 0.220 207 0.196 MI = 0.05U.4u2 1o.378 0.361 0.330 0.305 Jo.286 0.269 0.256 0.0145100ar All
00.0 2 0.294 10.279 0.254 0.236 0.220 207 0.196 MI = 0.05 U.4u2 1o.378 0.361 0.330 0.305 Jo.286 0.269 0.256 0.01 45 100 ar All...
5 answers
Hint: You may want to use Pearsonsr and - a scatter plotIPerson IAgeISessions14011I3oI1o127124I1212o
Hint: You may want to use Pearsonsr and - a scatter plot IPerson IAge ISessions 140 11 I3o I1o 127 124 I12 12o...

-- 0.021267--