5

5. Find ahl equation of the plane containing (1,0,0) and the line (1,0,2) + t(3,2,1)....

Question

5. Find ahl equation of the plane containing (1,0,0) and the line (1,0,2) + t(3,2,1).

5. Find ahl equation of the plane containing (1,0,0) and the line (1,0,2) + t(3,2,1).



Answers

Verify that the plane $x-y+5 z=10$ and the line $\mathbf{r}(t)=$ $\langle 1,0,1\rangle+ t(-2,1,1)$ intersect at $P=(-3,2,3) .$

In this question. We want to write the equation of a plane and it is told that the plane is Madeline to a plane and that learn is the works minus life less threes. That is, it was true. Then we can see that the normal vector of this plane is why minus day plus three K. So this is the normal welcome of this plane. And it is told that both the planes our Madeline and since they are parallel it means that they should have same normal websites. So we can say that the normal vector of the required plane should also be crystal. This weapon that is why I minus J. Lost creek. No we can see that we have the normal vector. It means we have values of A. B. And see No we are given with the point from which the plane is passing And that point is 1 -20. So you can see that destroys the value of x not why not? And they're not. And with the help of the normal vector and points. The equation of plan is aim to x minus x. Note, Let's be into why-? Why not? Let's see into their minus they're not. It was 20. So we are going to subscribe ut's values here, Values of ACC 2 -1, 3. So two years then -1 and then three and X -X. Note is X -1. Why-? Why not? Is white list too? And that minor said notice that zero. So further solving it we can say that we get here two X minus two minus by minus two plus three. That is because +20. This the words networks minus Y plus three. That is because +24. So this is the answer of this question here. Thank you.

In this question. When you go on about a question, the plan since then it contended your point, Ah contended upon extra Why's there was zero and it has a number of it the ego to a PC. Then we have a formal on the plan will be many times X minus X Sarah does be times y minus. Why zero just saved temps to the Manistee zero. You go to zero and now in this question, were given the plan. It contains a three point awakening as I PC here. But my ego too. So 11 be equal to no 101 Say you could you know, 110 And now we only got one porn already. So we need to find a number that you find a number of it. The first I need to find a better. Maybe it would equal June the one man 10 Also the better PC you get ICO 2011 of one on now from here The number on the plan which they go to the A P because with the PC. So if we cost them, let me go. June uh, one. And this one will be in the one. And this way you go to want this. Well, so that's gonna be the no more. Then we can use the point here, then the question when looking for will be one times X minus zero plus one times one minus one plus one Time C minus one equal to zero. We get the X plus y plus C, they go to minus one minus one, minus two in country to

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.

According to the question, we need to find the equation off the plane. We have given the plane passing through points bossing through the points. He's one coma, zero coma, three and zero comma for comma two and van Coma Van Coma one. We know that the question off the plane passing through the three known call in your points the soul. The formula is x minus X one y minus. Violent zag Minor Zevulun x two minus X one White to minus violin. Zach to minus zero even x three miners x one. Why three Minus violin. Zack three. Minus Zegra When we find out there determine its is equal to zero, we get the equation off the plane. Then we have three points known Colin. Your reject the equation off the pain easily by using these metrics did dominates property the no. Then their value is x one by 10 even and the value is X two y two thereto and the value is extremely white tree and Zach tree we have all value is given when we substitute all values in this Matics matter dominates, we get the result ease ex my nose X one is one, then one via I minus via one is zero these up to Duke zero zed Miners said One is three weeks of to to the value of Z advice and extra is zero minus X funnies. Von vie to is four minus y bunnies. Zero Zet, please. Two miners there. One is three rules is up procured All values X trees one minus X one is one vai trees one minus. Why one is vehicle Zach Trees one minus 01 is three. Then we find out it's dominate first ofall the soul and we convert is easy value X minus one. Why? They're minus three minus one four minus one Tzeitel one minus. Do that's easy to Seoul. Determinate resolve Determinate X minus one First drawing. First column these elements and minus eight plus one minus vie No plus zag miners three minus one is equal to zero. When you saw then X minus one minus salan minus vie into two blows Seg minus three Multiply with minus fun When we multiplied minus sellin X blows Salan minus do way Minor zed plus three is equal to zero When we sold sellin X minus two way Mine is egg plus 10 is equal to zero, and we get the final result. Ease selling ICS minus two way. Mina's egg is equal to minus. Then when we eliminate all miners are cancel each other we get. The result is sellin X bolos to weigh. Plus, Zed is equal to 10.


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