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QUESTiON 10tne praseuto oukskde Iet plane tninq hiqh alritude Ialla buow atmocphoric ptubsuro Iha n Insldo tha plnte mat 0a Praruurzed Drolt tho plabungen Whai Is t...

Question

QUESTiON 10tne praseuto oukskde Iet plane tninq hiqh alritude Ialla buow atmocphoric ptubsuro Iha n Insldo tha plnte mat 0a Praruurzed Drolt tho plabungen Whai Is tno prossuro mMT Obpnaree- cointhi ancrnalBi rending 584 mmHa? 0.768 #1m 0,77 0,788 mmhaquestion 11Lhich mihumatici oquilon shoud bu Ustd? pola Modlams Lsing Charlas $ Law 0MiVi - T2V2 0 PzVi PiVz0 P0 noneoi Ina Ebor8

QUESTiON 10 tne praseuto oukskde Iet plane tninq hiqh alritude Ialla buow atmocphoric ptubsuro Iha n Insldo tha plnte mat 0a Praruurzed Drolt tho plabungen Whai Is tno prossuro mMT Obpnaree- cointhi ancrnalBi rending 584 mmHa? 0.768 #1m 0,77 0,788 mmha question 11 Lhich mihumatici oquilon shoud bu Ustd? pola Modlams Lsing Charlas $ Law 0MiVi - T2V2 0 PzVi PiVz 0 P 0 noneoi Ina Ebor8



Answers

$21-26$ Equations of Planes Find an equation of the plane
that passes through the points $P, Q,$ and $R .$
$$P(6,-2,1), \quad Q(5,-3,-1), \quad R(7,0,0)$$

In this question we have to find evacuation of a plane that is passing through three points. Let the points are entered by abc that are 100 These given to us 13,010 and three point is given to us. That is 001. Now, first of all I am going to find here baby and where they see for there to be able to subtract from B. So we can see that we got here 0 -1 i. And then 1 0 J. And then they don't mind. Us did. Okay. Means it can be written as minus I plus day. Similarly, A C can be made. If we subtract promise C then you can see we get here zero minus one I & 0 0 J. and 1- said, Okay, this provides me minus. I will ask a No. We need the normal vector of Lynn And for that we have to make the cross product of the DNA. See they will provide the normal vector. Okay, So we have to take the help of the determinant. I didn't get put the components of a b minus 110 And from here put the components of the letter That is -10 and one. Now after expanding it, we get the normal vector that is denoted by director and here. And we can see that we get it. I I plus J plus K. Okay. In other words, it can be recognize one from a one comma one. No, it is told that The plane is passing from three points. Take any of the point that it's Consider 100. And now with the help of this normal vector at this point we can right the equation of them. I can say that in towards minors. That's not. Let's be into Why minus? Why not? Let's see into that minors that notice it was too little substitute here. Well of abc that is 111 so we don't hear of one. And then again one. Okay. And then again one and then it's minus X. No it's not this one. And why not decide not? R. Zero, so why minus zero And Santa zero. Office simplifying it. You can see with their care. X plus Y. Let's study. It was +21 So this is the except of the given question here. Okay. Thank

The the angle between the plane that goes through these two points three points 100010 and 001. And the Y. Z plane. So we have to find the angle between the normal vectors. And you do that by doing the coastline of data is the dot product of the vectors over the product of the magnitudes. All right. So we've got to find the normal vectors. Okay, if you'll remember from some problem above, if you have the intercepts, then you can write the equation like this. That's a that's a Z right there. Okay. Where A. Is one, B is one and C is one. So we get X plus Y plus Z equals one. So the normal vector for the 1st 1 is 1 1. 1 can the Y Z plane. Okay. Here's the Y. Z plane vector normal to it would be the victor. I Or 100. Okay, so then the cosine of the angle between them is the dot product which is one plus zero plus zero over the magnitude which is the square to three times the square to one. Okay, so the coastline of data equals Square root of three. Reciprocal .5774. So tha tha is the inverse co sign of that Sewing radiance. About .96 radiance and in degrees .5774 Inverse Post Line. About 55°

This exercise, we're told that the weight of an object above the surface of the earth is W. Equals r squared w not over our plus H squared R. Is the radius of the earth. And w not is the weight of the aggregate sea level. So we know that our is 63 80 kilometers. So we want to know that if the object weighs 200 in the sea level, we want to know when it's height is less than 100. So the way we're going to calculate this is we know that we'll have r squared which is 63 80 squared, I'm omega not about the tight at sea level, sometimes 200 divided by um are so 63 80 each, the height above sea level green card plus X. And that value is going to be squared. Now that we have this graph, we now want to evaluate the graph and find when the weight is going to be less than 100 newtons. So looking at our inequality here, we see that the weight will be less than 100 men's. Once we reach an altitude of about, um, it be an altitude of about 2640 3, 2642.5 feet above sea level.

I know everyone in this question. We have to find the question off plane when three points on a plane or given now from the general equation off plane. We know how to write the equation off plane when one point on a plane is given and a normal vector to the plane is given. But in this case, we three points on a plane or given. So from thes three point, we can find a normal vector. We will draw to Victor's on the plane and take their cross product, which will give us the normal vector to the plane. So first of all ages look att those three points, that is be six common one common one que. That is three common to Goma zero and our that is zero comma, zero comma zero no, first of all, find the vector P Q. That is negative. Three one negative one and only. Just find the vector p r. That is, they do six Negative one negative one. No need to state the cross product of these two victors. They did 31 negative one Negatives x 91 inevitable that is equal to negative. Thio close three d those 90. So now consider Ooh, this as a normal vector and this as a point on the line. Now we will use the general equation off plane that is off this form into its minus X mort lesbian, too. Why minus why not? Please see induce it minus said not equal to zero. We will use this equation where A, B and C are the components off normal vector. And it's not why not? And did not. Our three Carly needs off point on a plane. So let's plug in the values for this our kiss. And after plugging in the values we will get to ex mine, too minus twigs, bliss do you want plus nines it he called to CEO, and that's the answer.


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