5

1. (H points) Answer the following questions: points) Find A equation for the plane that contains the points (1.0.0). (0.1,3) and 20 (b) points) Find An equation fo...

Question

1. (H points) Answer the following questions: points) Find A equation for the plane that contains the points (1.0.0). (0.1,3) and 20 (b) points) Find An equation for the line passing through the point (0,0,0)and prallel to hoth of the planes r + "v+:= and 2r + v + 2:

1. (H points) Answer the following questions: points) Find A equation for the plane that contains the points (1.0.0). (0.1,3) and 20 (b) points) Find An equation for the line passing through the point (0,0,0)and prallel to hoth of the planes r + "v+:= and 2r + v + 2:



Answers

$21-26$ Equations of Planes Find an equation of the plane
that passes through the points $P, Q,$ and $R .$
$$P(2,0,0), \quad Q(0,2,-2), \quad R(0,0,4)$$

Here were given. We re kind of concern from the question of man, we will need todo element here. The 1st 1 will be the born on the plan Extra wives on disease. Oh, and now another component will be the normal Better under from I, b and C So and then the question of the plan will be any times X minus Xterra, plus the times Why minus wiser plus C times a minus is the ICO Judah so and now given in the question here were given the three point B minus 211 that we have the Jew three. And so we have the 101 now in it to find a norm of factor here, not charger. Let me The nanny defined it on me I b c And then they try to find out that I be first. So what, We're gonna go do the job? One Joe, Also, we can find a better job. We see in were ICO June the one man ist u minus, Joe. So every cost times you get a normal that every culture that I be cost one there but the bc and then we should get Eagle Joe, the minus Jew and then usually beat you and the media Terminal B minus fall minus six every six years. And the last one will be minus four minus one. OK, minus five. So given the normal now and a point we contend upon, see, now there found a question on the plan. It would be Jew. Tam's X minus one plus six times requirement is, though minus five times a minus one ju zero we consume. If I get it you ANC's man ist your plus six y minus five c plus five coaches are Are gonna Joe Express Knicks? Why? Minus five z Enrico June minus three.

Nice in this Berlin your give entry points P history over to coma or common native to you, that is netted. One. How come on Tau zero And our that is never if one how come a zero comma two on what we want is an equation of the plane that passes through the points P Q and R So let's get started. So first of all, let's Quincy there this, uh, vector the better be cume onda vector p. R. So we think about the cross product off the factors that start this new factor and waiting about these, um, this new vector Deneuve actress perpendicular to both the vector P Q and A vector Pierre under, for it is perpendicular to the plane to P. Q and R. So if we remember Doc Cross product is defined in the next way. Just as I wrote before. So for the windows were more that we can get that the components off these new bedroom. So first of all, we just need to find out back the components off pick Yu NPR individually. So let's do that soapy cume. It is just tree over to minus and never early one house that is just for house. That he's just on that is just too. And we have four minus two. That is just too on narrative to minus zero is just a young girl to my No. Zero is just never victim. So those are the components off pick you now, PR. We have, uh, tree over to my nurse nearly 1/2 thatis again too. Then we have four minus zero that he's just wore on. We have narrated to minors to the majors and nearly poor. So those were the components off this factor. And now that we have the components of those two factors, we can get that, um, these the cross product off the back trippy que onda better pr. So let's just do that. Um, yeah, so following the formula, we have a two times be tree that he's Neri bait and we have my nose A tree. Me too. So that is just, um a tree is narrated to be, too is for so that he's netted a woman. We have a tree, b B one so that use nearly four minus a one between. So that is never a I. Finally, we have Hey, one thing's be too. That is a times Ah, do they? Minus 382 things be want bodies for so we can simplify those components. So we know that netted a a minus native ate that He's just a zero then 94 minus narrative a minus negative eight home that he's just for, um for minus eight is judged for so yeah, but now we have the components over these normal back her on DDE. Yeah, it is really important to how these neural better so we can get out who's, you know, off the plane. So let's just, uh, remember, let's continue on his page. Uh, let me, uh it raises. I'm really sorry. Yeah. So it is important to mention that if we have a point, let's say ex not. Why not? See? Not. And we have a normal vector, ABC then that plane that contains these points on these normal vector is described in the following way. Uh, eight times x minus X not blessed be. Thanks. Bye. Minus Why not Pelosi? Tanzi may know Xena on that is equal to zero, so we can't We can't take this into account on estar finding the equation off the plane so we can use of reference his point. The 00.0.3 over a tomb for my four common narrative too. There's just righted. Itwas tree over too. Well, not for culminated two on. We can't just rewrite the components off or back. Drew. And those components were zero coma for coma or and we conserve. Stick to those valleys e to our formula. So yeah, let's do that. It will be zero times X minus tree over too. Blows four kinds. Why minus four? Loves four diamonds e minus. Negative doom. And that is just it. Well, do zero. Yeah, I forgot. This parenthesis is so this is this will be just 20 on days. Will be for why? I know 16 up close for Z. Let me just re cried. Theis, please. Yeah, plus for Z Um yeah, No, anything negative is reciprocity of So we'll have. We will have z plus. Do so for if we applied distribution, we will have thes plus eight. So four times two is just ate so well have we will have a and that is just equal to zero. So again we can isolate the wise and disease. There's just Rick Rightist for awhile. I pose for sea and we can add 16 in both size and sub strapped a dreamboat site. We will get 16 mines, eh? And that is just a I'm Finally, we're gonna divide everything by four. So we will have ah, for at why I'm sorry. Blust Z on a divided by four is just too. Yeah, This is a red equation off the plane is why plus c equals tomb. Mmm. So, yeah, I does he answer why? Plus Z is equal to do. That's the question off the plane, so thank you for

This exercise were given the points p before ordinates 200 Cube coordinates zero to negative two and our with Corden at 00 for and we want to find an equation for the plane that passes through these three points. First, we'll find two points that lie on this plane. Uh, let's take PR and P. Q. So P R is equal to zero when it's to their mind. Zero for minus zero, which is equal to negative 204 and P two is equal to 01 is to zero. Um, to my eyes zero negative 210 which is equal to negative two too negative, too. Okay, now that we have these, we can find the cross product and they're cross product is perpendicular to both of them. Therefore, it's normal to the plane that we're looking for. So we have the determinant that is the cross product, which is negative. 204 and negative too. Ah, too negative, too. Let's calculate this. So have zero for two. Negative, too. This is a coefficient of I minus negative two for living a too limited too. And this is the coefficient of J and negative to zero. Number two to this isn't cooperation, K. So we have following would have zero minus eight I minus four my plus eight because this is we subtract This is negative. So four plus eight j plus negative for my zero of Okay, so this is equal to negative eight I minus 12 j who minus four k which is equal to negative. A negative 12. Negative for Okay, so this is one normal Lecter, But we can use and will use it along the point p to plug in values. So for our equation, we have negative eight x minus two plus or other minus 12. Uihlein zero minus four Z minus zero is equal to zero. We can multiply these out or other weaken first divide by negative four so that we have for two x money's, too Ah, plus three. Why my zero close 00 ankles. Zero. And now we can multiply this out two x minus four plus three y plus z z zero and we can move before to you outside to obtain her final answer to wax. Plus three y plus Z is equal before and this is your final answer

And find the equal sound a plan. And that had been through the three point We connect with me that I at the 103 and upon pain and, uh, so fast you and the ponsi 111 So you notify the equipment plan we need to have the normal vector. So first, them I will find a better be now and then we say we didn't need you Turned a big win a minus. I was minus one four minus one. Similarly, we can find that the BCS well, we get equal to the one monastery minus one, and then the normal bitter It will be the crossbow that under to better a b and B c And they were getting going to if we cost them. And now we got minus all, uh, minus film industry money. Seven on, uh, that's the needle term. You'd be one because one would be to someone is to So, uh, three miners. Ah, fall becomes a minus one here. So wait. We found the normal better on. We can take one point here less I and then we can get a question on the plan. They were ico Judah minus seven times when the X minus one minus two times Y minus zero minus Quantum's as the ministry because you zero it will multiply inside and kind of minus seven X plus seven minus two Y minus Z blustery coaches zero are gonna minus seven expense to my ministry if we go to the Manus Tan.


Similar Solved Questions

5 answers
3. Let L1 be the line in R" defined by the following general equations:I - 2 = 22x _ y = 3and let Lz be the line defined by the following general equations: ~y + 2z = -1I -y +2 = 1. Are L1 and Lz the same line? Explain why O why not_
3. Let L1 be the line in R" defined by the following general equations: I - 2 = 2 2x _ y = 3 and let Lz be the line defined by the following general equations: ~y + 2z = -1 I -y +2 = 1. Are L1 and Lz the same line? Explain why O why not_...
5 answers
The ground state term symbol for the free Fe?- ionis 6D
The ground state term symbol for the free Fe?- ionis 6D...
5 answers
Civeu:12 I 630 10.75. H "'/115.0 =0.01 claim: Ho (") (2 points) Clearly state Ho and H , and identify the type of test Ho H(b) 2 points) Fiud ac name all related critical values, draw the distribution. and clearly mark and shade the critical region(s).
civeu: 12 I 630 10.75. H "'/115.0 =0.01 claim: Ho (") (2 points) Clearly state Ho and H , and identify the type of test Ho H (b) 2 points) Fiud ac name all related critical values, draw the distribution. and clearly mark and shade the critical region(s)....
5 answers
Uhis Question:For the following function; find (a) ((9), (b) 4 2x + 2 #*+9 f(x) = itx=9and (c) I(a)(a) Find the value of f(9).0(9) (Type an integer or _ simplified fraction )(D) Find the valuoo(-%): {-#-0 (Type an integer or & simplified Iraction ) Find Ine value of f(a).Iaz9ila) =ifa =9Enter your answer In each of the answer boxos
Uhis Question: For the following function; find (a) ((9), (b) 4 2x + 2 #*+9 f(x) = itx=9 and (c) I(a) (a) Find the value of f(9). 0(9) (Type an integer or _ simplified fraction ) (D) Find the valuo o(-%): {-#-0 (Type an integer or & simplified Iraction ) Find Ine value of f(a). Iaz9 ila) = ifa ...
5 answers
Point) This problem is similar to one from your textbook:f() = -712 +t+8Find the equation of the line tangent to the graph of f(t) att = 7.Enter the equation of the tangent line here (in terms of the variable t):
point) This problem is similar to one from your textbook: f() = -712 +t+8 Find the equation of the line tangent to the graph of f(t) att = 7. Enter the equation of the tangent line here (in terms of the variable t):...
5 answers
(q What What Calculate grinding Question the its Wheel 9 acceleration lineaular 35 (20 speed of velocity points) diameter point point on 2 rad /s_ rotates the edge 2200 the rpm grinding wheel? wheel?
(q What What Calculate grinding Question the its Wheel 9 acceleration lineaular 35 (20 speed of velocity points) diameter point point on 2 rad /s_ rotates the edge 2200 the rpm grinding wheel? wheel?...
2 answers
2 T1 3 9 0 2 ~2 2 ~1 Question 2 (14 points) A = 1 2 0 3 9 0 0 1 0 1 Find basis for column space of A; Col(A): b) Find basis for row space of A; Row(A). Find a basis for null space of A; Null(A): What are the rank(A) and the nullity(A)? Do the column vectors of A span R4?
2 T1 3 9 0 2 ~2 2 ~1 Question 2 (14 points) A = 1 2 0 3 9 0 0 1 0 1 Find basis for column space of A; Col(A): b) Find basis for row space of A; Row(A). Find a basis for null space of A; Null(A): What are the rank(A) and the nullity(A)? Do the column vectors of A span R4?...
5 answers
A) J Iv-Idzb1 6' e + 1 8+ z dz6f9 dxd)'f (84)' dc
a) J Iv-Idz b1 6' e + 1 8+ z dz 6f9 dx d) 'f (84)' dc...
5 answers
In the figure 81 = 2.46 V,82 - 113V,R1 4.200,R2 = 2.380,R3 3.77 02,and both batteries are ideal. What is the rate at which energy is dissipated in (a) R1: (b) Rz, and (c) R3? What is the power of (d) battery 1 and (e) battery 2?NumberUnits(b) NumberUnitsNumberUnits(d) NumberUnits(e) NumberUnits
In the figure 81 = 2.46 V,82 - 113V,R1 4.200,R2 = 2.380,R3 3.77 02,and both batteries are ideal. What is the rate at which energy is dissipated in (a) R1: (b) Rz, and (c) R3? What is the power of (d) battery 1 and (e) battery 2? Number Units (b) Number Units Number Units (d) Number Units (e) Number ...
5 answers
Wha compound represents base In (he following chemnical reaction? HSO4 HO m HSO Hyom 0 HzSO4 0 b Hpoc HSO4HzOt
Wha compound represents base In (he following chemnical reaction? HSO4 HO m HSO Hyom 0 HzSO4 0 b Hpo c HSO4 HzOt...
5 answers
Represent the area bounded by the curve y = 8x3 4x, Ihe x-axis and (he vertical line
Represent the area bounded by the curve y = 8x3 4x, Ihe x-axis and (he vertical line...
5 answers
What would be the product of the following reaction sequence?OH1) PCl; 7i) C6Ho, AICI; jii) Zn(Hg), HCL, heat
What would be the product of the following reaction sequence? OH 1) PCl; 7i) C6Ho, AICI; jii) Zn(Hg), HCL, heat...
5 answers
Five bundles of pencils contain the quantitiesbelow. BundleNumber of pencilsA8B6C4D10E6a. How many different samples of size 2 bundles each arethere?b. List all possible samples of size 2 and compute themean of each sample.BundlesMean Number of Pencilsc. Calculate the population mean and compare it to themean of the sampling distribution.
Five bundles of pencils contain the quantities below. Bundle Number of pencils A 8 B 6 C 4 D 10 E 6 a. How many different samples of size 2 bundles each are there? b. List all possible samples of size 2 and compute the mean of each sample. Bundles Mean Number of Pencils c. Calculate the populatio...
5 answers
13. Find the Laplace transform of(2 pts) 3sin(2t) (b) (5 pts) u(t - 3)t2 , where u(t) is the unit step function. Show your work Label where you use tables.
13. Find the Laplace transform of (2 pts) 3sin(2t) (b) (5 pts) u(t - 3)t2 , where u(t) is the unit step function. Show your work Label where you use tables....

-- 0.026426--