choose-a-set-s-of-four-distinct-points-in-mathbbr3-such-that-aff-s-is-the-plane-2-x_1x_2-3-x_312-jus

Name: choose a set s of four distinct points in mathbbr3 such that aff s is the plane 2 x_1x_2 3 x_312 jus
Uploaded: 2019-08-24
Duration: 3 min 50 s
Channel: Numerade
Description: Choose a set $S$ of four distinct points in $\mathbb{R}^{3}$ such that aff $S$ is the plane $2 x_{1}+x_{2}-3 x_{3}=12 .$ Justify your work.

Question

Choose a set $S$ of four distinct points in $\mathbb{R}^{3}$ such that aff $S$ is the plane $2 x_{1}+x_{2}-3 x_{3}=12 .$ Justify your work.

Gideon Idumah · Accepted Answer

we solve this question so we because we&#x27;re told to choose, is sets s or four dick stints points in out for you. So we do these by choosing four points from the blame Sue X one plus X two minus three X Terry. Of course it&#x27;s solved. So duds at lists we need three off them our notes Kulina. That is why we don&#x27;t we want want to pick up the street at the local inn is because if the points kulina, the uh oh would be in line I&#x27;m not a plane. So sure that those four points known is Karina just into victory. Because if you picked suit as a possibility that they are not soon maybe Kulina sold to pick the three points. So pick three points. That&#x27;s ah, holding that are not Kalinda. So, for example, we can sets x one equal to X to quart zero on dhe off. We do that off. This implies out of mine a story ex Terry recorded solve on, then extra because of minus four. So with these women, three anos cortina. So we can also said so this is one point second points you can set X one equal to X Treaty Court Zero. This would imply that&#x27;s when you plug that in. This would imply because X 10 extra is there a Thomas ext Sue Records. It solved. I&#x27;m for the foot start points because sets ext Su equal to X tree records zero. This was implied. And after two ex want records to solve and an excellent quarter to six now we need 1/4 points. Um, for the fourth points, we can just pick any points for the fourth for the fourth points. Choose whatever points you want to say. We can choose X one equal to X to the quarter one. You can pick anything you want. So this would be Sue Lost. One minor story. Ex Terry Quarter solve. This implies our ex Terry Quarts of minus three. So this implies that&#x27;s in total. The points we compete so we can choose as to be sick. Ward. So for the first point, you have x 10 extra 000 minus fall, the second point x 10 extra reserve and we got extra to be solved. Similarly, we odd 600 and then lastly, we have 11 minus

Michael Jacobsen · Answer

in this example, we&#x27;re going to consider the Plain X three equals five that lives in the space are three. Our goal here is to find a set s consisting of vectors, V one, V two V three such that the a fine hole of this s will result in the same plane X three equals five. So to start out, let&#x27;s begin building vectors V one and the first requirement such that the ATF fine whole generates a plane is that all the vectors must come from the plane itself, which means X three must always be equal to five. So it&#x27;s right v one v two and the three such that five is the last entry. Now, whatever we put in the 1st 2 entries, at least we know that all of these vectors lie in that plane. Now we can pick just about any set of vectors in this plane. They must be distinct. Otherwise, that fine hold will generate a single point, not the plane. So I could start off with, say, 10 Then we could put in possibly a 20 and noticed that if we have a 10 and a 20 then in the plain, X three equals five thes two points will go through. These two points will go through the line in that plane. If we do say 30 all three points V one v two V three are going to lie on the same exact line in the plane. This is problematic since in this case, if all three points are Colin near the F find whole would generate a line and not a plane. So we need to be very careful with the last factor. We just need to insist that if we were to plot these on the plane, extra equals five. Not all points lie on the same line. We might try something along the lines of, say, a 10 to change it up. Now all three points are not Colin ear on the plain. X three equals five And this implies next that the I find hole of the city s where v one v two v three are as to find generates the plane. X three equals five

Ankit Gupta · Answer

we have given a portion three X plus two y plus toe plus through there is equal to 12 and we need to sketch the plane the president did by the lean Eric question that list full points. That&#x27;s like end up it. First we need to skin the plan playing. Then when it list up, four point of is is flying this plane, so finding the points first. So for that, just taking some values at why is equal to zero Leo and is that is equal to zero so we can die. The X is equal to Otwell or from here we can get over Lou effects that is full. And the point will become the point. From here begin simply right, fool. And now that X is equal, does it&#x27;ll? And that is equal, though. Zero. So we will get here Where Lou off. Why? Which is sick? The point will become zero six little Now what will we will do here? So at exit weirdo zero And why is it Porto zero? So we&#x27;ll get the value of said so we can get here. That is a weirdo, say and point here will get 00 six. So now from this weekend, let&#x27;s get a graph which is here. So just plotting this Lord, please. Three points on the three D coordinate plain. So we get up graph, We&#x27;ll have a graph like this. So this is a graph. This is a light. So here, recondite possible point that can lead possible plan would be to 30 1st another 1203 zero for two. There are 24 This is a possible point we can see here.

Himanshu Kushwaha · Answer

given three equations by six explains to Dr Bliss toe that line and its place to wear this toe. There is a group of three I need to find the point discovered for all these three days. So does he. Was a substitution Italy first. So by is 1/4 to 6 minus for their as it to do this value by another two to bring the questions in to worry about. So I get explorers doing toe six miners or there less so their physical tonight express well minus AIDS. It less given three equations by place or they&#x27;re visible to six explains to worthless executable nine and X place to worthless. That is equal to three. We need to find a point which is going under these. Do you please. So that is you. The suspicion who I heard by six minus poor there for their your vagina that we question subindex version into relievers. So I get explosive. The will do by Leslie. It is a physical nine x place went toe. Six Niners or their plus need their physical. Tonight I get explain well minus exit. Leslie exit is equal to 900 x value was minus three from this information. No point insensible to minus three. And by is a good rapport place. You know what that says? You go to my history and buy it for six minus 14 in the Tory question Spore equation. World explorers to wear plus through their visible with three Xs minus three. Just +2126 minus four. Then plus they&#x27;re visible toe three. So I minus replaced. Well, finest aids it plus lose it physical to three. So I did minus exit nine. Minus sits. There is it Will do three. So I guess six physical to 60 and then is it will do well to advise equal to six minus hold. It is a good six minus border into one physical dough Do so they My point is minus b to find one

Himanshu Kushwaha · Answer

you&#x27;re given three equations. X plus three zero is a good +23 Byatt was or there isn&#x27;t going to six X plus right? Plus six. There is a greedy nine. We need to find a home. One point it is we need to find the point, which is goingto all these three. Please. We have three equations and three variables. Notice all the questions from here. I get X is equal. Total three minus sees it and I get why is it will do six miles or that that does put dualism bits and by in the whole equation. So I get three minus 30 plus six minus four there plus six. There is a good tonight, so I get nine minus seven plus six is minus that is equal to night. For the moment, that is zero. So I get access three minus three into zero is equal to three. I get by s six miles. Pour into zero is equal to six. So there&#x27;s other point. It&#x27;s 36

Sriparna Bhattacharjee · Answer

According to the question, we have to find the equation of the plane that passes through the .314 and contains the line of intersection of the plains. Given by the equation number one express two, Y plus trees that equal to one. And equation two is two, X minus Y plus Z is equal to minus three. So in order to find the equation of the plane according to the given equation and point given in the question. So firstly they have given a point, let&#x27;s say the point is E. And the coordinates are given us 31 fools. And in order to find the question of the plane we first have to find a normal victor And using these points we can find the equation of the plane. So in order to find the normal victim to the plane we have to find another. Mhm two points in the plane using the equation one and two. Therefore if X equal to zero then Equation one and 2 becomes do Y plus tris ID Equal to one and why minus way less? That is equal to -3. And by solving the simultaneous equation continues the two variables Y and there we can find out available. So if we multiply equation do with two then It will become -2. Y Plus two, said is equal to In place of minus treat will become -6. So solving mm The equations we can get by adding distributions, we can get that pi Z is equal to minus five, therefore Z is equal to minus one and in order to find out the value of why we can put the value of set in any of these equations that is minus Y plus said equal to minus three. Immigration to if you put the value of $0.00 -1 then it will become Why is equal to 3 -1, that is equal to two. Therefore we got another points. Let us say it be which has coordinates zero, two and minus one. Yes. Yeah. Yeah. And in order to find another point in the plane, you have to consider the value of the Is equal to zero. Therefore equation one and 2 becomes X plus to way equal to one and two weeks -Y Equal to -3. So in order to equate this to value and catholic the values of the variables multiplying equation two by two. We get This way efficient as four. This is too And this is six. Therefore adding these two equations. We can get the value of X, that is five X equal to minus five. Therefore The value of x equal to -1. And putting the value of X. In any of the equations we can get the value of Y. That is x minus y two, X minus Y Is equal to -3. Therefore go into minus one minus white. Well to minus three and therefore the value of why is equal to minus two plus three, that is equal to one. Therefore we got the coordinates of another point. Let&#x27;s suppose the point. Because they see these coordinates are minus one one and zero. Therefore The three points in the plane. Oh point E 314 point b 0 to -1 buoyancy -110. Therefore in order to find the normal vector to the plane we have to find the two lines from these points that is line A B vector is equal to 0 -3. I gap Plus 2 -1. Jacob Plus -1 -4 K Cab. This is equal to -3 icap plus Jacob -5 K cups and this is equal to victor once opposed. And another line vector that is a C vector is equal to -1 -3, icap plus 1 -1. Jacob 0 -4. Kick up this is equal to minus minus four. I grew up less zero, Jacob less mm That is -4. Kick up. And let us suppose this vector is equal to be to cap. Then in order to find the normal vector to the plane You have to find the cross product of B one. And we do this is equal to Ichabod Jacob Jacob and The values are -3, -5 And -4, 0. And minus for therefore the after calculating this cross product, the normal vector will be equal to minus four Icap. Let&#x27;s eat Jacob, my bliss for kick up. So from this we can calculate the equation on the plane as follows. That is Yeah. Yeah. By the formula To find the equation of the planet is in two X minus egg zero plus being two Y minus Y zero Plus seen to that zero equal to zero, bear A. B. C. Although mhm coefficient of direction vectors for the normal victor. That is this is A. This is B. This is C. And egg zero, Y. Zero and zero. Although point in the Mhm len here this point is equal to 314 as given in the question. Okay so the aggression of the plane is equal to yeah minus four X minus three. Let&#x27;s eat. Why? Minus one last four. That minus four Is equal to zero. After solving the situation, we can derive the final equation of the plane as minus X plus two. Y. Let&#x27;s said equal to three. And this is the required equation under lean for the given question.

Problem

Let $S$ be an affine subset of $\mathbb{R}^{n},$ …

Problem 18 Medium Difficulty

Choose a set $S$ of four distinct points in $\mathbb{R}^{3}$ such that aff $S$ is the plane $2 x_{1}+x_{2}-3 x_{3}=12 .$ Justify your work.

Answer

an affine set
$S=\left\{\left(\begin{array}{l}{6} \\ {3} \\ {1}\end{array}\right),\left(\begin{array}{l}{5} \\ {8} \\ {2}\end{array}\right),\left(\begin{array}{l}{2} \\ {8} \\ {0}\end{array}\right),\left(\begin{array}{c}{1} \\ {13} \\ {1}\end{array}\right)\right\}$

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David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications

Catherine R.

Anna Marie V.

Heather Z.

Joseph L.

Vectors Intro

Vector Basics - Example 1

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an affine set$S=\left\{\left(\begin{array}{l}{6} \\ {3} \\ {1}\end{array}\right),\left(\begin{array}{l}{5} \\ {8} \\ {2}\end{array}\right),\left(\begin{array}{l}{2} \\ {8} \\ {0}\end{array}\right),\left(\begin{array}{c}{1} \\ {13} \\ {1}\end{array}\right)\right\}$

Linear Algebra and Its Applications

Catherine R.

Anna Marie V.

Heather Z.

Joseph L.

Vectors Intro

Vector Basics - Example 1

David C. Lay, Steven R. Lay, Judi J. McDonaldLinear Algebra and Its Applications

Catherine R.

Anna Marie V.

Heather Z.

Joseph L.

an affine set
$S=\left\{\left(\begin{array}{l}{6} \\ {3} \\ {1}\end{array}\right),\left(\begin{array}{l}{5} \\ {8} \\ {2}\end{array}\right),\left(\begin{array}{l}{2} \\ {8} \\ {0}\end{array}\right),\left(\begin{array}{c}{1} \\ {13} \\ {1}\end{array}\right)\right\}$

David C. Lay, Steven R. Lay, Judi J. McDonald

Linear Algebra and Its Applications