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Point) The lines Li(t) = (2t _ 5,5,3 _ t) and Lz(s) = (21 + 4s,5,20 + 4s) intersectWhen t2When $2At the Point2...

Question

Point) The lines Li(t) = (2t _ 5,5,3 _ t) and Lz(s) = (21 + 4s,5,20 + 4s) intersectWhen t2When $2At the Point2

point) The lines Li(t) = (2t _ 5,5,3 _ t) and Lz(s) = (21 + 4s,5,20 + 4s) intersect When t 2 When $ 2 At the Point 2



Answers

Determine whether the lines $\mathbf{r}_{1}(t)=\langle 2,1,1\rangle+ t\langle- 4,0,1\rangle$ and $\mathbf{r}_{2}(s)=\langle- 4,1,5\rangle+ s\langle 2,1,-2\rangle$ intersect, and if so, find the point of
intersection.

It was a question of the plan. Why couldn't minus two and like ocean are Nico agenda to the last one Minus They blessed far t minus six And yeah, notice that you find upon with the sections this could be the thanks This will be the why and just you be that see And we see that Because we're even the one Could you Ministerial here implies that the man ist tu minus they impress for an Afghanistan that being in continuous 6 1006 we can get the parliament in the sexually you'll be So what did they equal to six into this Corcemar line here? So six ago been we wouldn't sigh minus six plus far Six minutes explode And then we get Nico two under the thing Glennis ju zero

In the question given the equation virtualized, the first line is 13 equals ju the 011 aan den plus the tee times the +112 And we have the art too. But here would ask her equal to the +203 plus as times the one for For now we want to find the intersection between them. So when did you get the I want Thio Put them equal to the R two s, so doesn't oblige them. We should have the system of questions. Here we have the zero plus the most echo into the two plus asked are then one plus the must equal to the zero plus for ask, then one plus two the most equal to the three plus four ask and then they try to serve the system in question. Now here to serve it, we take the first on the second and the third one. Here we do the subjection and we do so different guns zero then minus three equal to the minus three plus zero doesn't oblige. That team is equal to the three. When going to take three, you can block back to the first equation here, You get the answer. They were equal to the three minus two, equal to one. And now we need to make so that you go to certify the same problem intersection. So it will be good for the T equal to three. We will bring it to the R 13 that were equal to the 011 plus the three times +112 So we should get equal to the point. Here will be three and then one plus three. Could you far one plus six equal to seven. And now let's try to check if the ethical to one are too one, it will be good to the 203 plus the 144 So if we add them up with a skeptical to the 34 and seven so they much of each other here. Therefore, we have the problem. In the section will be this point here

Listen here, given the question that July's So we have the I won t e code you The man is 1 to 2 plus the tee times when the four months to one and we have the Thio use the verbal as here Nico to the 011 on Then plus when the asked times when the +201 and let's try to find the intersection between them. So we want to put our won t they go to the aren't us so it means that we should have the minus one plus four Day was equally do the zero plus to ask and then to manage tooty must equal to the one plus their own hands. Then we have the two plus the most equal to the one plus as and now here From the second question, we see that we can get ah managed to day It means then that you Dave equal to the one it means that you could you have when we have to take what you have we can look into the last question here we have the two plus half because you want plus asked therefore asked me Go Joe, the one plus a half and then continue to the end of do so. Then we tried Thio and we put into the first question here we can get no minus one a minus one plus for they will be a half equal to zero plus two times s will be equal to the three and of two. So we see on deciding an equal attuned, uh, Tu minus one equal to one and for this time get equal to directory. So clearly they're not ICO therefore means that on one day does not intersect. There are two yes.

To the given problem. We want to consider If we have the lion, x equals negative two teen rq custody. We have y equals three p. Yes. And then we have Z equals four key or four plus T. It's all right. And in this case we are looking at the .066. So we want to know if this point is on the line. Well, consider the fact that if we get zero as our X coordinate. That that must mean that T equals positive too. If T equals two, then why would equal six? Which it does and Z would equal six which it does. So in this case that point is on the line. Now let's consider 235. We here we see that if this is too that means he must equal four. If T is four, this gives us why is equal to 12 and Z is equal to eight. So because of that this point is not on the line.


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