Find feF- di utere Cisa crce of radus 2 in the plane z+y+ = = 9, centered at (2, 2, 5) and oriented clockatse when viewed hom the origin, - 2yi 2rj + 3(y a|

Q: Find the point where the helix r(t) = (cos(t), sin(t), t) intersects the plane z = (х, у, 2) %3D

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Q: Find the area of the surface. The portion of the plane z = 24 - 3x - 2y in the first octant

A: ⇒Given:-  Equation of plane                      z=24-3x-2y  in 1stoctant In intercept form,…

Q: Find parametrizations for the lines in which the planes x + y + z = 1, x + y = 2

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Q: Find the distance between the point and the plane. 19. (0,0,0) and 2x+3y+z12 20. (2,8,4) and 2x+…

A: a) given point is (0,0,0)  plane is 2x+3y+z=12 find the distance between the point and the plane  b)…

Q: Show by Vector mothads that th ditonce hom fhe fornt P.(Xx, Y,, Z) to the plane Ax -+By+cz-D26 t of…

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Q: The area of the plane z = 2x + 1 above the disk of radius 1 centered at the origin is (а) 4л. (b)…

A: As we know, z=fx,y defines a surface in xyz-space.  Formula for the surface area of the surface…

Q: 5a. Consider the right square pyramid with a horizontal plane intersecting the pyramid halfway up…

A: The horizontal plane will be parallel to the base of the pyramid.

Q: For what positive value of c is the acute angle between the plane containing the points A(0,0,1),…

A: The equation of the plane passing through the three non-colinear points x1,y1,z1, x2,y2,z2, and…

Q: Compute the surface area of the ellipse that lies on the plane z=11-3x+2y and inside the cylinder…

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Q: Fin He ara at tHe surface af the portion oF Hae Plane 2= 5-2X -9y

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Q: Find parametrizations The portion of the plane 4x + 2y + 4z = 12 that lies above the square 0<=…

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Q: Find the area of the surface. The part of the plane  z = 3 + 2x + 5y  that lies above the rectangle…

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Q: Find the symmetrical point of point P(-1,-3,5) with respect to the plane D:3x-2y+z+6=0

A: Point P(-1,-3,5)  plane D:3x-2y+z+6=0

Q: Find a plane through the origin that is perpendicular to the plane M: 2x + 3y + z = 12 in a right…

A: Given equation of plane is

Q: Evaluate ff. xyz ds, over that part of a sphere of two units radius and centre at the origin Which…

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Q: Find the distance from the a. x-axis to the plane z = 3. b. origin to the plane 2 = z - x. c. point…

A: a) z=3 is parallel to x axis. It is 3 units above x axis. ( Refer to the diagram)Answer: 3

Q: Find the equatioa of tangeut plane to the surface + 2y? + 3: = 21 which is puraliel to the plane 2r…

A: parallel to plane 2x+4y+6z = 3      surface x2 + 2y2 + 3z2 = 21     Let  F = x2 +2 y2 + 3z2 = 21  we…

Q: What is the intersection of the plane x+2y+z =0 and the line (x, y,z) = (0,1,2)+ k(–1,1,2), kER?

A: Consider the equation of plane x+2y+z=0 and the equation of line x,y,z=0,1,2+k-1,1,2. Find the…

Q: Find the area of the surface. The portion of the plane z = 6 - 3x – 2y in the first octant

A: We need to find the area of the portion of the plane z=6-3x-2y in the first octant. Let f(x, y) =…

Q: What cross-section cannot be formed by intersecting a plane with a right cylinder? Campbol OM…

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Q: Find the symmetrical point of point P(1, 3, 4) with respect to the plane D:3x-2y+z+6=0.

A: Symmetrical point at plane problem....

Q: Find a formula for the distance from the point P(x, y, z) to the (a) xy-plane (b) yz-plane (c)…

A: Distance between two points x1, y1, z1 and x2, y2, z2 is given by x2-x12+y2-y12+z2-z12.

Q: Find the area of the cap cut from the top of the sphere x2 + y2 + z2 = 1 by the plane z = sqrt(2)/2.

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Q: Show thata perojective plane of gives 0nder indeed BİBD (+n+l, n+),1)

A: We need to show that the projective plane of order n indeed gives a BIBD (n2+n+1,n+1,1)

Q: Calculate fc((3x + 5y) i + (3x + 4y) j) - dr where C is the circular path with center (a, b) and…

A: According to the greens theorem:

Q: Find the surface area of the part of the plane z = 4+ 7x + 6y that lies above the rectangle [1, 6] ×…

A: We can use integral calculus to find the surface area of the part of the plane above the given…

Q: Find the distance from the point B = (1, 0, 2) to the plane P whose general equation is x + y -z =…

A: Equation of the plane is Given point is

Q: Find the surface area of the part of the plane 7+ 2x + 5y that lies above the rectangle [1, 4] x [0,…

A: Given that  Z=7+2x+5y To find the area of the surface of the plane that lies above the rectangle

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: Use triple iutegral in reitanqular coordinates +to tindd te nass of. sphere with den a ensing S こス…

A: mass = density * volumem        = massδ         = densityV        =…

Q: Find the surface area of the part of the plane 3x + 2y + 4z = 24 that lies in the first octant…

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Q: Compute the surface area of the ellipse that lies on the plane z = 11 – 3x + 2y and inside the…

A: The surface area of the surface given by z=f(x,y) where (x,y) is a point from the region D in the…

Q: Find the distance between the point and the plane. 19. (0,0,0) and 2x+3y+z=12

A: As there are multiple questions, the first one (19) is solved here.

Q: Find the angle between the two planes 3x − y + z = 7 ,  4x + 6y + 3z = 2 and find a set of…

A: Given, two planes 3x − y + z = 7 ,  4x + 6y + 3z = 2  we have to find the angle between the two…

Q: Write down a parametrization r(u, v) for the portion of the plane x - y+ z = 3 that lies inside the…

A: r(u, v) = ( u cos v , u sin v,  3 - u cos v + u sin v)  Where u € [0, 1]           v€ [ 0,2π]

Q: Find the surface area of that part of the plane 6x + 8y + z = 7 that lies inside the elliptic…

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Q: Find the surface area of that part of the plane 8x + 9y + z = 8 that lies inside the elliptic…

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Q: Find the area of the cap cut from the top of the sphere x2 + y2 + z2 = 1 by the plane z = √2/2.

A: Given equation of sphere is    x2+y2+z2=1     And the equation of plane is  z=22=12 But we know that…

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: Find a parametrization for the line segment beginning at P, and ending at P2. P (2,-3,2) and P2(0, –…

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Q: Find the surface area of the part of the plane 3x + 3y+ z = 9 that lies above the triangle formed by…

A: In the question we have to find the surface area of the plane.

Q: A tangent plane to the ellipsoid x². y? a b2 meets the axes in A, B, C. Show that the envelope of…

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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…

A: consider the following equations  f(x,y,z)=x2yz+1                                  (1)h(x,y,z)=z-1…

Q: Find the area of the surface. The part of the plane z = 7+ 2x + 3y that lies above the rectangle [0,…

A: We have to find the area of the surface of the given problem.

Q: Bounded by the paraboloid z = 10 – 3x? – 3y2 and the plane z = 4 (using polar coordinates)

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Q: Find the surface area of the part of the plane z = 4 + 6x + 2y that lies above the rectangle [1, 4]…

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Q: Find a vector parametrization for the quarter-ellipse from (5, 0, 6) to (0, −2, 6) centered at (0,…

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Coordinate Geometry

Coordinate geometry, also known as analytic geometry or Cartesian geometry in classical mathematics, is a type of geometry that is studied using a coordinate system. Coordinate geometry is a branch of mathematics that describes the position of points on a plane using an ordered pair of numbers called coordinates.