The pyramid is bounded below by the xy plane above by the plane x+y+z=3 and on the sides by the xz- and yz- planes

Q: Let L be a line which passes through the point (-7,0,1) and is perpendicular to the plane x + 2y +…

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Q: Let L be a line which passes through the point (-4,0, 1) and is perpendicular to the plane x + 2y +…

A: Please refer the attached image for complete solution.

Q: 2) The distance between the parallel planes ax + by + cz + d1 = 0 and |d1-d2| ax+by+cz + d2 = 0 is…

A: We find required equations of plane parallel to given plane.

Q: Let p be a plane which contains the point Q(1,2,3) and the intersection line of the planes: 2x+3y-…

A: Concept: 1. The equation of plane passing through the line of intersection of the given planes…

Q: Evaluate / x2 zdS, where S is the part of the plane z = 4+ 3x + y above the rectangle [0, 4] x [0,…

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Q: Find the dimensions of the largest rectangular box in the first octant (x, y, z > 0) with one corner…

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Q: Let L be a line which passes through the point (-8, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: Find the line of intersection of the given planes. 4x + y-z = 0 and 2x - y + 3z 4 %3D

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Q: Bounded by the coordinate planes and the plane 3x + 2y + z = 6

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Q: 4. Find a plane through Po(2, 1, –1) and perpendicular to the line of in- tersection of the planes…

A: Since you have posted multiple questions in this question which are not interlinked so I have solved…

Q: Find the distance between the planes x + 3y – 2z = 3 and 2x - y - z = 4. %3D

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Q: 3. Among all the points on the graph of z = 10 – x² – y² above the plane x + 2y + 3z = 0, find the…

A: As per our guidelines we are supposed to answer only one question at a time. So I am solving the…

Q: Find the maximum volume of a box that is resting on the xy-plane with one vertex at the origin and…

A: Given the plane is 3x+4y+2z=12

Q: 45. Find the distance from the plane x + 2y + 6z = 1 to the plane x + 2y + 6z = 10.

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Q: 37 Find the equaton of a plane that contains the point (4, -3, –1) and is perpendicular to the…

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Q: A(n)________ is the collection of points in the plane the difference of whose distances from two…

A: The given statement is "A(n)________ is the collection of points in the plane the difference of…

Q: 12 above the Find the surface area of the portion of the plane 2r + 6y + 3z triangular region in the…

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Q: Let L be a line which passes through the point (-4, 0, 1) and is perpendicular to the plane x + 2y +…

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Q: Find the maximum volume of a box that is resting on the xy-plane with one vertex at the origin and…

A: Given, equation of the plane is  7x + 6y + 2z = 18 => 2z = 18 - 6y - 7x Therefore, z = ( 1/2)(18…

Q: 2. Find a unitvedctor with positive z-component porpendcular to the plane 2xt2y-2=3 Z-C

A: We will find out the required value.

Q: 39. The plane that passes through the point (1, 5, 1) and is perpendicular to the planes 2x +y - 2z…

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Q: 3) . Find the centroid of the upper half of a sphere of radius 1, that is, of the set of points in…

A: Given the upper half of the sphere with radius 1, that is x2+y2+z2=1,z≥0. Find the centroid x¯,y¯,z¯…

Q: 5. Evaluate 2XZds where S is the part of the plane - 2x +4+Z =3 over the triangle with bounds…

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Q: 4 and the plane Find the point on the curve of intersection of the paraboloid x- + y- x - y + 2z = 0…

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Q: Find the distance from the plane x + 2y + 6z = 1 to the plane Q1 x + 2y + 6z = 10. %3D

A: 1. Given equation of plane is : x+2y+6z=1     ....1 x+2y+6z=10      .....2 Both the equation of…

Q: Find the Largest open rectangle in the plane in which the hypotheses of Existence and uniqueness…

A: Answer

Q: 4. Find the area of the surface S where S is the part of the plane z = 3x +y that lies above the…

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Q: The point (-2,0,8) is. A. In die xy-vlak O In the xy-plane B. In die yz-vlak O In the yz-plane C. In…

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Q: Find the extreme values of ƒ(x, y, z) = x2yz + 1 on the intersection of the plane z = 1 with the…

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Q: Let C be the cubic region delimited by the coordinate planes and by the planes x = 2 y=2 and z=2 in…

A: the planes x = 2 y=2 and z=2 in the first octant.

Q: 1. Find the distance between the two planes - 2y + z=4 and z-2y+ :-1 HI

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Q: Find the line of intersection of the planes x- y- 2z 1 and a +y+z=-1. Lütfen birini seçin: a.L : x =…

A: Given equation of plane is x−y−2z=1 and x+y+z=−1. We have to find the line of intersection of the…

Q: Find the intersections of the line x = -2, y = 4 + 2t, z = -3 + t with the xy-plane, the xz-plane,…

A: Given x=-2, y=4+2t, z=-3+tfor finding intersection with xy-plane , set z-coordinate…

Q: Among all the points on the graph of z = 10-x2 -y² that lie above the plane r+2y+3z = 0, ind the…

A: Given that z=10-x2-y2 and x+2y+3z=0 Find the point which is farthest from the plane.

Q: 2. Find the eanation of the plane Containing the point (2,3,3)'and the line Of intersÉCtion 'of the…

A: We have to find the equation of plane containing the point (2, 3, 3) and the line of intersection of…

Q: Let L be a line which passes through the point (-6,0, 1) and is perpendicular to the plane x + 2y…

A: Direction ratio of Line is < 1,2,6> Write equation of straight line and solve it with plane to…

Q: Let L be a line which passes through the point (-5,0, 1) and is perpendicular to the plane x + 2y +…

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Q: A cube of cheese from Italy with edge measure of 1 was cut by Mickey using a plane in a manner that…

A: Let us assume the the cordinates OA= OB= OC= 1

Q: Does the plane x = 5 have a trace in the yz-plane? Explain.

A: Given: The plane is: x=5 We have to determine the given plane is trace in the yz-plane and explain

Q: Q:- find of the the line of interscetion plane given by 3X +6y -S2=-3 f the plane -2x + 79 -2=24

A: 3x+6y-5z+3=0 -2x+7y-z-24=0 Let z=t 3x +6y = 5t-3 -2x+7y = t+24

Q: Let L be a line which passes through the point (-7,0, 1) and is perpendicular to the plane x + 2y +…

A: Here we find the equation of line L and also find the intersecting point of line and plane.

Q: Find the area of on of the triangle that can drawn between the planes 3x – 6y – 2z = 15 - and 2r + y…

A: For any triangle that will lie between two planes, one point has to lie on a plane and the other two…

Q: Let S be the triangular prism with the triangular face in the plane y-3 removed. Let C be the…

A: Given curl F→=xi^-yj^ and the given plane is y=3 So, ϕx,y,z=3j^ Therefore, calculate curl F→·n^ curl…

Q: The distance between the parallel planes ax + by + cz + d1 = 0 and ax + by + cz + d2 = 0 is D =…

A: topic = planes

Q: Using projection(s), find the distance between the following planes: Plane 1: 5x + 2y −3z = 7, Plane…

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Q: Find the area of the surface. The part of the plane z = 4 + 3x + 2y that lies above the rectangle…

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Q: 4. Find the point of intersection of the plane z= 4 and the line L={ (x, y, z) | x= 4 + 3t, y=-1-2t,…

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Q: Find the area of the surface. The part of the plane z = 8 + 5x + 2y that lies above the rectangle…

A: Area of the surface z=f(x,y) A(s)=∬1+fx2+fy2f(x,y)=8+5x+2yfx=5fy=2

Q: 2) The solid lies between planes perpendicular to the x-axis at x = -2 and x = 2. The cross sections…

A: Let's find.

Q: Find a plane containing the point (3,-7,8) and the tine of intersection of the planes-4z +4y + 4z =…

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