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1 Example #2: Exumple #I: What { What is the relationship Try Anothor Vorelon relationship between 1 Ihe specilic 1 1 1 0f(25JR)-2 | Il...

Question

1 Example #2: Exumple #I: What { What is the relationship Try Anothor Vorelon relationship between 1 Ihe specilic 1 1 1 0f(25JR)-2 | Il

1 Example #2: Exumple #I: What { What is the relationship Try Anothor Vorelon relationship between 1 Ihe specilic 1 1 1 0f(25JR)-2 | Il



Answers

$$ \begin{array}{l} \left[1_{1}, \mathrm{~m}_{1}, \mathrm{n}_{1}\right],\left[\mathrm{l}_{2}, \mathrm{~m}_{2}, \mathrm{n}_{2}\right] \text { are the direction cosines of two lines inclined at an angle } \theta \text { to each other. Show that the line }\\ \text { with direction cosines }\left[\frac{I_{1}+1_{2}}{2 \cos \frac{\theta}{2}}, \frac{m_{1}+m_{2}}{2 \cos \frac{\theta}{2}}, \frac{n_{1}+n_{2}}{2 \cos \frac{\theta}{2}}\right] \text { bisects the angle between the two given lines. } \end{array} $$

So we have blue Victoza you envy such that? Ah, factor you. It's recorded minus six Momo six. But the V The secret minus one No. One. So it's one comma minus one and we could find on the door put of the victims so you don't v c Kotal mine at six Cold six Marty one on the minus one. This value comes to be minus 61 That's six tango minus one. This brand you see quarter nine US six minus six. It's just equal to minus two were on. We will find out the anger they convict us left every building that vision cost teeth It's given by you dark the upon magnitude of you by the magnitude of B and this is equal minus two Well born. A little more off magnetic review is 96 where that's six grand. You get that base blueprint that off one square that's minus one square. This value sequel minus do well for 72 surface express the basic 72 and the route this is equal managed to will for market thing the that this within the square work there is what people this value so pretty minus upon will. The belt is minus one since, uh, the bandage off cost you guys manage from so Tito this week? Okay. Course. And thus Oh, minus one. Just be quartile. One in three degrees. Careful, though. Radio dark work of the witness is minus 12 and grew up there and ordered in the that does this to support one and critically.

Let's start by finding distance one. So using the distance formula, we have a square root of the change in X one minus zero squared plus the change and why I m one minus zero squared. And that would be the square root of one squared, which is one plus m. One squared and then we have distance to which would be the square root of the change in X one minus zero squared plus a change And why am to minus zero squared? And just like the previous one, we would get the square root of one plus m two squared. Okay, Now, according to the Pythagorean Theorem, since we have a right triangle here, the distance between the two points, uh, right here would be the put. That would be the high pot news of the right triangle. So we have distance, one squared plus distance, two squared equals, and I'll call that distance. Three distance, three squared. So let's go ahead and substitute some values in there. Distance one square toe, one plus m. One squared, and that needs to be squared and then distance to square to one plus m. Two squared, and that needs to be squared equals distance three squared in distance. Three would be the change in in white coordinates M one minus in two. And we'll square that as well. Okay, so let's go ahead and simplify. So we have some squares of square roots that leaves us with one plus m one plus one plus m two squared on that and squared on that. And then we can foil this quantity here and we get m one squared minus two times M one m two plus M two squared. Okay, Now notice that we have an M one squared at an M. Two scored on both sides. We can subtract in, those will cancel. And the rest of it is one plus 12 equals negative to m one m two. Let's divide both sides by negative, too. And we get negative. One equals m one m two. Now what that means is that when you multiply those two slopes, you get negative one. So there, opposite reciprocal. We could say that if we wanted to buy both sides by m one, we could say that M two is negative, one divided by M one. So they are opposite reciprocal. And that makes sense because these lines were perpendicular

So today we're gonna prove the tangent of Half is gonna eat will sign of half a over coastline of half eight. And to know that all we need is one simple substitution. So we know that the tangent of all angles data is equal to the sign of all angles data over the coastline of all angles, data. And so if we do a substitution that half of A is equal to an angle Fada and we plug that into this equation, it becomes that one. And so really, what this means is that half of a should be treated like any other angle and that the tangent of half a will equal the sign of half of a divided by the coastline of Hap obey because the half of a still in angle thanks for watching

Okay. So first That's fine. D. one did you? In terms of I'm one I'm too okay. They want you close square roots off. I'm one squared plus Y squared D two Echoes. Square it off. I'm too uh squared plus one square. Okay. So then you uh I think we're on the Syrian to find a really a shame. P. T. M. One M. Two. Okay. So I know that I'm 1 -22 squared because the one squared plus D. Two square. Okay, so I have a more than minus M two squared because I'm one squared plus one plus I. M two squared plus four. So I'm well squared. One is two times I'm one time 72 plus I'm two squared because M Y squared plus having to square close to. Okay, so cancel out, cancel out so minus two times and one times two equals two. So and more than times I'm too Because last one. Okay, so this is a relationship between M. One and M. Two or you can write em one equals minus one over M two. Okay?


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