b) a dr+(x+yz) dy+(ry- VE) dz, C is the boundary of the part of the plane 3r+2y+z in the first octant. (Compare to section 16.8, problem 8.) c) a = ry dr+ yz dy + za dz, C is the boundary of the part of the paraboloid z = 1- x2 in the first octant. (Compare to section 16.8, problem 9.)

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Q: D

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Q: Find the area of the band cut from the paraboloid x2 + y2 - z = 0 by the planes z = 2 and z = 6.

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Q: Example 8. Evaluate , A.n ds where A=(x+y)i-2j+2yzk and S is the surface of the plane 2x + y + 2z =…

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Q: C, D are coplanar points. A', B', C', D' are their projections respectively on the y-

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Q: Classify the surface: 1-z = 3y? + 4z? ,2

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Q: 6 Consider points P and Q in the x-y plane, with P = (1,0) and Q (0,1). The line integral %3D %3D Q…

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Q: d) If S is projected onto the x - y plane, what is the shape of the resulting projection?

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Q: Sketch the surfaces CYLINDERS z = y2 - 1

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Q: Consider the quadric ax2 + y2 + 4z2 + x + 6y−4z = −a−10 where a is a parameter. Find all the values…

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Q: If A = 18zî – 12j + 3yk then find SS,A.ñds where S is the surface of the plane %3D 2x + 3y + 6z = 12…

A: Given, surface S: 2x+3y+6z=12           and                       A→=18zi^-12j^+3yk^

Q: FIND THE AREA OF THE SURFACE FOR THE PORTION OF THE PARABOLOID Z = 49-x² - y² IN THE FIRST OCTANT

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Q: 1. Find the area of the surface the part of the plane 3x + 2y + z = 6 that lies on the first octant

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Q: 2. Find the area of the part of the sphere x² + y² + z² = 4z that lies inside the paraboloid z = x²…

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Q: Show that the system of confocal and co-axial parabolas y²-4a(a+x) is self orthogonal, where a is…

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Q: 6. What is an equation for the largest ball centred at (0,0, 1) that can fit in the paraboloid z…

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Q: 6. In Section 12.5, you learned that the distance from a point (ro, Yo, zo) to a plane ax+by+cz = d…

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Q: Let C be the boundaries of the ellipse +=1 taken in the 9 16 counterclockwise direction. A…

A: We have to check

Q: Consider the three-dimensional Euclidean space with coordinates x, y and z. The intersection of the…

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Q: C is the intersection curve between the paraboloid z=x²+y² and

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Q: 1)calculate a*yz dædydz where D is the rectangular parallelepiped 1< « < 2,1 < y < 2,1 < z < 5

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Q: Sketch the surfaces HYPERBOLOIDS (y2/4) - (x2/4) - z2 = 1

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Q: .2 The surface z? = 1 is a 25 - - 36 hyperboloid of one sheet. Select one: OTrue OFalse

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Q: Find the center C and the radius a for the spheres 3x2 + 3y2 + 3z2 + 2y - 2z = 9

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Q: (B) Integrate paraboloid (x, y, z)=- 2x-²-2-0 by the plane x=1. over the surface cut from the end of…

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Q: A designer proposed using a paraboloid S,: x² +y² = z as the basis of a container design. However,…

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Q: If a parametric surface given by r1(u, v) = f(u, v)i + g(u, v)j+ h(u,v)k and –1< u<1, –2 < v< 2, has…

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Q: Find the point on the curve of intersection of the paraboloid x² • y² + 2z=4 and the plane x-y+ 2z…

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Q: Calculate ff A.n ds If A = yi + 2xj – zk and S is a 2x + y = 6 plane surface in the first octane cut…

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Q: determine a and b as to make the cylinder y^2=4ax orthogonal to the ellipsoid at point (1,2,1)

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Q: Find %3D as if F(x, y, z) = 2xi+2yj+2zk and S is the part of the paraboloid z = 4-x-y lying above…

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Q: Find the points on the hyperboloid 9x^2  - 45y^2 + 5z^2 = 45 where the tangent plane is parallel to…

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Q: show that a=(2x^2+8xy^2z)i+(3x^3y-3xy)j-(4y^2z^2+2x^3z)k is not a solenoidal but b=(xyz^2.A) is…

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Q: The part of the plane 3x + 2y +: - 6 that lies in the first octant

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Q: If A = 18zî – 12ĵ + 3yk then find Jſ, A.ñ ds where S is the surface of the plane %3D 2x + 3y + 6z =…

A: Note "As per our company guidelines we are supposed to answer ?️only first question. Kindly repost…

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Q: paraboloid z= 1 - (2x^2) -y^2 and plane z + x + y =4 find the shortest distance between them

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

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Q: Prove that the surface of the given equation is an ellipsoid. Hence, determine its center. 9x +4y…

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Q: If & is the solid tetrahedron with vertices (0, 0, 0), (3, 0, 0), (0, 5, 0) and (0, 0, 4) then: z dV…

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Q: Compute 5xy ds, where S is the surface of the tetrahedron with sides z = 0, y = 0, x + z = 1, and x…

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Q: I am having trouble solving this.

A: To find the area of the overlap between the interior of the ellipses given below.

Q: The part of the surface z-1+ 3x + 2y that lies above the triangle with vertices (0, 0), (0, 1). and…

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Q: 1. Find the Point the Plane X + 3y +27 = 6 that on %3D is nearest to the orig in.

A: To find- Find the point on the plane x + 3y + 2z = 6 that is nearest to the origin.