Question
Find the equation af the taugent lite the cuIVe y=r (0,0)the giren point y=VT-x, (1,0)
Find the equation af the taugent lite the cuIVe y=r (0,0) the giren point y=VT-x, (1,0)
Answers
Find an equation of the plane that passes through the given points. $$ (-2,1,1),(0,2,3), \text { and }(1,0,-1) $$
In this question we have to find evacuation of plane that is passing through three points. I'm going to write this given three points. Let denote them by abc 8. 342. And the point is having coordinates minus two comma one, comma zero and three point is having 0 to 1. First of all. With the help of these points, we are going to find vector lady and we're crazy that lies in the plane. We have to subtract it from B. So we got minus two minus three I and then 1 -4 Day and then they don't mind. Us too. Okay, So you can see with that year -5 Y or it can be simply uh readiness in the form of minus five comma minus three comma minus two. Okay. Now, similarly to find a say, we have to subtract a promise see. So we got to get 0 -3 I And then to -4 J. And then 1 -2 came. So we can say that we got here -3 and then -2 and then -1. So these are the vectors that lie in the plane. Now we need the normal vector of the pain. That is where to land. We can see that This should be it was to cross product of B and a C. So we have to make the cross product with the help of the determinant that takes I take in the first four. In the second one minus five minus three minus two in the third of the components. Obviously that is minus three minus two minus one. Now after making the expansion, We got here the normal vector and that is it was 2 -1 less a day less gay. Or it can be written as minus one, comma one, comma one. Now we are given with three points. We can take help of any point Letter states help zero. Obama Obama won. And now we can write the evacuation of playing with the help of these two informations that can say into x minus x. Not let's be into why minus why not last see into that minus that noted it was a little substitute. Well okay we see that is minus 11 and one. So you can see that you're -1 and then one and then again one and now substitute value of the given point. That is 0 to 1. So it's minus zero y minus two And they're the -1. So we can see that. After simplifying it we go to bed minus X. That's why I -2 -1. If it was too zero we can see this wirelessly x minus light. Mine is that And last today the past 20. So this is the regulation of required plenty of. Okay thank you.
Victor, A. B. As well as victor A. C. So A. B. Is equals 25 Mana zero which is five 0 -3 which is -3 And so on and so forth. To get him a -8 day and then I see will be equal to for zero 16. So I'm going to rename these Just to make our lives easier. This will be a. one and this will be B. One. So now that we have our two victims, we need to find the cross products between the two So that we can find our normal vector. So this is equals two I. G. Key. Okay so first show we have I shake a second, you'll have A. Y. A. one which is equals 2 5 -3 -8. 3rd row will have 4016 in this. If you actually do the um the calculation using the determinant, my thought You will end up with -4. The eight I minus G. Into 112 plus K. Mhm. Times 12. Okay so now this is our normal ah the normal victor. Yeah. Right and I'll just rewrite it here is E. B. C. Which is equals two minus 48 -112 and 12. Yeah. So ticket the equation of the plane, we're going to use the general formula. Uh But ultimately we need a point on the plane which is represented by X zero, Y zero and Z zero. And we also need the normal vector which we have right here. So our A. B. N. C. You find them here here and here. So what is lived now is to substitute our values. Okay so Um a is equal to -48 Into X -0 0 plus um B. Which is -112 into Y -3 class. Um See which is 12 into z minus negative seven. And we equated to zero if we um expand this and simplify it, what we actually end up with is We end up with -48, X -112. Why? Plus 12 Z Plus 4 20, which is equals to zero. And this is the equation Yeah.
The increase in the line could be. Why equals M X plus B where Emma's you're still open? Be answered by intercept. You could start off by finding the slope, which is flying to minus 11 over x two minus x one. Or in this case, whatever one just one serene or equations going to be. Why equals X Class B? You got what B is. Plug in one of your points for X and Y and sulfur beat. So this case, we can plug in zero for X and zero for Why get the fact that B equals zero? So your question is very straightforward. It's just why equals X?
In this question with a condom and the question the line why equals m x plus b. When I am, he will stand found a slump and we go to the white ju minus y one on the extreme minus x one. Be here stands funder. Why intercept Andi in this question here were given the two point The first one will be the 00 The second one will be the minus 15 And from here we can identify the X one y one x two y two. Therefore, we can find a slump and equal to why two minutes? My one on the x two minus next one that we get equal to the five minister all understand, Minister, or they will get equal to five for minus one are equal to minus five. And then we confined block into the formula Here again the Y ICO Children minus five x plus b To figure out the B, we use the first point now, so it means that why equal to zero? And the X, also equal to zero plus B doesn't realize that the P equals zero square. They found out why we're looking for would be. Why? Equal to the minus five x Not you. Scandal line on the craft. You could be easy here. So we have here will be X and the Y here. This will be the zero here. We see the first point to be 00 will be this origin here. The next point behind the minus 15 So it will be here. So what? You need to join them up. And this woman that question on the Y in coaching minus five X.