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12. [-/1 Points]DETAILSSCALC8 12.5.040_MY NOTESFind an equation of the plane_ The plane that passes through the line f Intersection of the planes x - 2 = 2 and32 = ...

Question

12. [-/1 Points]DETAILSSCALC8 12.5.040_MY NOTESFind an equation of the plane_ The plane that passes through the line f Intersection of the planes x - 2 = 2 and32 = 2 and Is perpendicular to the plane x + Y - 2z = 4Submit Answer

12. [-/1 Points] DETAILS SCALC8 12.5.040_ MY NOTES Find an equation of the plane_ The plane that passes through the line f Intersection of the planes x - 2 = 2 and 32 = 2 and Is perpendicular to the plane x + Y - 2z = 4 Submit Answer



Answers

$21-32=$ Find an equation of the plane.
The plane that passes through the line of intersection of the
planes $x-z=1$ and $y+2 z=3$ and is perpendicular to
the plane $x+y-2 z=1$

So we want to use the information we're given to find the equation of a plane. Um So for this problem in particular, the key is to find two important vectors. And then those vectors will allow you to find the normal vector, which you can then use to substitute into this equation. Um Given the point that has coordinates A BNC. So what we have here is remembering that the equation of a plane which passes through the intersection of P one equals zero. Mp to equal zero. Well look like P one plus lambda, P two equals zero. So with this in mind we have X -Z -1. That's r. p one plus lambda times, Y plus two, Z minus three equals zero. Then combining everything. What we end up getting as a result is X plus lambda, Y plus choo lambda minus one. Z minus three. Lambda plus one equals zero. Then we can write this as a dot product because we know the dot product. Normal vectors is zero. So that's gonna be one. Land to λ -1 dot 11 to negative two. That's an equal zero. Then based on this, we end up getting three minus three. Lambda equals zero, so lambda equals one, substituting that value back into our original equation. We end up getting X plus Y plus Z minus four equals zero. So our final answer of the plane, I was going to be X plus Y plus Z equals four.

In the question they're asking to find the equation of the plane that passes through .151 and is perpendicular to two planes. Given by the equation. To explain why -2 that equal to two and express trees that equal to four. So from the two equations of the plane that is perpendicular to the plane of the given question. We can find the normal vectors from the equations of the perpendicular planes. So the first normal vector is equal to two, I cab plus Jacob minus to kick up. And the second normal vector from the second equation is equal to icap plus three Jacob, it's a zero Jacob Last three. Kick up. So from these two normal vectors you can find them normal vector of the plane asking the question so it will be equal to cross product of these two normal vectors together that is equal to in one cap. Cross into cap that is equal to we will put the values of anyone into in the Stephen 2, -2 and 103. And after computing the cross product of anyone and enter the final value of n. Cap is equal to three. I gap minus a Jacob minus Jacob. And in order to find the equation of the plane. As asking the question, we'll look at another point that is given in the question 15. Fun. And using the normal victor. And the point given the question, we can find the equation of the plane as follows, that is three into X -1 -8 into Y -5 -1 in two, 0 -1 is equal to zero. So the final value of this equation is three x -8 by Miner Said, Is equal to -38. And so this is the equation of the plane as asked from the question.

Question. When did you find the equation? The plan says that it going through the 0.151 and it's perpendicular to the two plans here. So will be the two x plus. Why minus two is equal to to another planet X plus three z equal too far Now, from the first plan, we can find a number and one Inco Jew to one month to and similarly, we can get into equal it, you know, 10 and three. And if we cost, then we get the number off at the on the plan we're looking for and one costs and to and we're equal. Jew have gone to three as six plus two equal to eight. So minus eight. Yeah, we have a minus one. Therefore, we got the normal better. And the pond therefore the plan we're looking for it will be three times X minus one minus eight. Hence why minus five minus one times Z minus one in coach is zero

The question. The plan so is that it contains upon minus one 21 and it contains the point of life is a section between the two plans. So be the experts y plus C equal to two different manner city. And then we have the two x plus minus wine plus three z equal to one. And here the first time we need to find the live intersection intersection between the two plans here. So, in what you do that, first of all, we would a line here. Then we do the audition, then we get a three X is when we cancel out. Then we have the plus to the ego to three, then doesn't implies that the three x we go to the three ministers e i. We have the X. We go to the one minus 200 trees e and that's gonna be the X now together. Why we can replay this, exhale into the first question. Then we get the, uh, we begin the one managed to out of trees e plus why? I'm honest, see, go to to. And then it means that why it was ego to the to ah minus one and then plus the plus two out of three is that then we should get a code, you know, one. And here we have the three. When we blast five out of threes that therefore we have the question of plan will be, uh the question that live in the section here will be X equal to one month, two out of three Z. We can write it as a D. Why equal to the one plus five out of three t and the ego to D and from the question of line here, we can find another point here. I will count it as a kill. And they were equal to the 110 as we send. Ah, a Swiss entity, could you? So we can have the dashing, but they and we multiply everything by. We get this one, we go thio the man a student of three 503 one. But let deal with the fraction, or we can get Oh, we can get a V Wonderful. I estimate three get nickel gentleman is 25 and three and therefore we will the next time we need to find a better be literally condenser. Be here. So we have a bit Big Gil. It will equal with you to minus one minus one. And we have the dietitian with the ve co two minus 253 So every cost that we get a number of it the any coaching, the big deal Glass window. But the V Do we get equal with you? Here we have money. Three plus five B two ah six minus juggle before minus four and 10 minus thio. Go to eight. How we can make it nicer to dividing everything by chewing on the one man is too far. Therefore, given the point, we can use the pawn kill here and we have the number of enter here. Therefore, the question of the plan It would be, uh thanks minus one minus two times Why? Minus one plus four times The man is zero equal to zero. Are we get the ex minister. Why? Plus Fonzie, it will equal with you. He'll have a minus one plus two equal with you the ones who have a minus one on the right hand side


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