Which of the following represents a plane surface whose x-, y-, and z-intercepts are a, b, and c respectively? O + + = 1 O x+ y+ z = abc O ax + by + cz = 1 O None of these

Q: 2. State the names of the following quadric surfaces. (a) The surface z = y² – 2x². (b) The surface…

A: a. this equation is in form of  as sign of A and B is opposite it is  Hyperbolic paraboloid

Q: Which of the following planes is tangent to the sphere x² + y + z' = 17 at the point (2, -2, 3)? %3D…

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Q: 1. Let F(x, y, z) = yi+ xj+ yzk and the surface S be the part of the paraboloid z = 4 – x2 – y? that…

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Q: Evaluate ff, F.dS, where F= (4xz, -y², yz) and Sis the surface of the cube bounded by the planes x =…

A: We will use divergence theorem to find given integral  ∫∫SF→dS →= ∫∫∫EdivF→ dV Where E is  solid…

Q: b) Use Gauss' theorem to evaluate ff F - ndS where F = (r - y)i + y²j+ (ry-y)k and o is the closed…

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Q: (b) A = 2pza, + 3z sin ø a, – 4p cos p a̟ and S is the surface of the wedge 0 0 < ¢ < 45°, 0 <z < 5

A: Let us solve the b part step by step with given A value

Q: Evaluate || F.ndS for the given F and o. (d) F(x, y, z) = xi+ yj+zk, o : the surface of the sphere…

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Q: Let M C R³ be the set obtained by rotating the circle {(x, 0, z) E R³ : (x – 2)² +2² = 1} about the…

A: Solution is given below

Q: Let P be the tangent plane to the surface z=x2+2y2 at the point Q=(-1,-1,3). Which of the following…

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Q: וווכu nt that enclosed by the surface z = 12 - x 2 - y 2 and the plane z = A. A=1

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Q: Let the surface S in R° parametrized by f : R? - → R³, f(u, v) = (v, 2uv, (u – 1)²) Find all (u, v)…

A: Given, that the surface S in R3 parametrized by   f:ℝ2→ℝ3fu,v=v,2uv,u−12 Now, find all the (u, v) at…

Q: 2. Evaluate F.ndS for the given F and o. (a F(x, y, z) = (x² + y)i+xyj- (2xz + y) k, o: the surface…

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Q: Which of the following quadratic surfaces describe an elliptic paraboloid shape ? OA. z = 2? – y² +…

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Q: a. Which of the following surface graphs represents f(x,y) = y²? OA.

A: Given, the surface                           z=f(x, y)=y2

Q: Use Stoke's theorem to evaluate F dr where F(x,y, z)=e-7i+ +e"k and C is the boundary of the part of…

A: Let Fx,y,z be a vector field and the surface S is bounded by a simple closed curve C. The Stoke's…

Q: A = xy'a, + y'a, + y°za, and S is the surface of the cuboid defined by 0 < x < 1, 0 < y < 1,0 < z <…

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Q: Let P be the tangent plane to the surface z-2x2+y2 at the point Q=(1,1,3). Which of the following…

A: Tangent plane to given surface

Q: Let P be the tangent plane to the surface z=x2+2y2 at the point Q=(-1,-1,3). Which of the following…

A: Given data: The given surface is z=x2+2y2. The point Q=(-1,-1,3).

Q: Evaluate F.ndS for the given F and o. (b) F(x, y, z) = (x² + y) i+ xyj– (2xz + y) k, o: the surface…

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Q: Evaluate V x F · N dS using Stoke's theorem, where F = (2x – y)I- yz }-ýzk and S is the upper half…

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Q: • What is/are the trace(s) of the surface (x – 1)? 22 = 1 on the rz-plane? 36 a. hyperbola b.…

A: For the given surface

Q: Sketch and label the level surfaces of g(r, y, z) =1-r² – y² for g = 0,-1,-2.

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Q: 1. Let a, b, c ER and let Sa,b,c = {(x, y, z): ax2 + by2 + cz²=0, x² + y² +2²=1}- (1a) For which…

A: Given: Sabc=(x,y,z): ax2+by2+cz2=0, x2+y2+z2=1 To find: the values a, b, c for which Sabc a regular…

Q: 9. Justify why the surfaces below are not pairwise locally isometric (a) Sphere S1 = {(x, y, 2) e R…

A: This is a problem of Differential Geometry.

Q: Let I- (VxG) ndo, where G(x.y,z)=(ze*-y,4x,z*) and S is the part ofi the surface z=/x²+6y²+1 that…

A: Given that Gx,y,z=zex-y,4x,z4. The surfaces are given by z=x2+6y2+1⇒z2=x2+6y2+1 that lies inside the…

Q: Let a, b and c be the last three digits of your student ID and let d=max(a,b,c). How many points are…

A: we have surface  z=6x2+y2 and plane 6x+y+z=0lets denote the surface equation as f(x,y,z)=z-6x2-y2and…

Q: 1. Find a parametric representation for the surface: the part of the sphere x2 + y? + z2 = 4 that…

A: According to the given information, It is required to calculate the parametric representation for…

Q: What is the surface area of the portion of the surface z= x?+y that lays over the triangle on xy-…

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Q: Which of the following is the equation of the tangent plane of the z = 3x^2+x-y^2+y surface at the…

A: Equation of tangent plane problem.....

Q: Which surface below is an elliptic paraboloid? O x^2 + y^2/4 - z^2 = 1 O z = -sqrt(x^2 + y^2) z =…

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Q: Describe and sketch the surfaces in space (R') defined by the following equa- tions: (a) y = -z +1…

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Q: Verify Stoke's Theorem for A = 3yî – xzj + yzk, where S is the surface of the paraboloid 2z = x + y?…

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Q: Let h, k, m, neR such that n > m >0. A general equation corresponding to the above surface is: A) (z…

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Q: let s is the curved surface of the cylinder x²÷a² + y²÷b²=1 0≤z≤c , then evaluate…

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Q: Evaluate | F-dS, where F(x, y, z) = (3y, –2x, –), %3D and S is the surface that is composed of the…

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Q: Let F(x, y, z) = -2yi – 3zj – 5xk and C be the circle x? + y? = 9 that forms the boundary of ơ in…

A: if you find my answer helpful please put thumbs up. thank you. the required solution is given below…

Q: Which of the following is an equation of a plane surface? O 2x +3y + 4z = 4 O 2x2 +3y + 4z = 4 O 2x…

A: To find:- Select an equation of plane surfacefrom given options

Q: The tangent plane to the graph of the surface z=In(x2+y?) at the point (1,0,0) contains point…

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Q: Let P be the tangent plane to the surface z=x2+2y2 at the point Q=(1,1,3). Which of the following…

A: We have to find the points on tangent plane .

Q: Find the points on the surface z =xy+36 that are closest to the origin. O a. (0, 0, 6) b. (0, 0, 36)…

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Q: The tangent plane to the graph of the surface z-In(x<+y) at the point (1,0,0) contains point (3,3,t)…

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Q: Which of the following is a defining equation for the tangential plane to the surface defined by…

A: To find  An equation for the tangential plane to the surface defined at the point (1, 1,1)

Q: (a) Given that F(x,y,z) = (3x² + 3y²)i – 2xyj + yzk, evaluate S, F·dr for which C is the boundary of…

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Q: 5. Prove that the surface E, = {(x, y, z)|a² + y² = 4} is locally isometric to the surface E2 = {(x,…

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Q: 2. State the names of the following quadric surfaces. (a) The surface z = y² – 2x². (b) The surface…

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Q: For the surface given by z= f(x,y) = 1 - 6z + y-3y? %3D %3D which of the following is true. Select…

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Q: Every level surface of f(x, y, z) = x + 2y+ 3z is a plane. Select one: O True O False

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Q: : The trace of the surface S x² Z = + 9. 4 in the plane z = 4 ||

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Q: Let P be the tangent plane to the surface z=x2+2y2 at the point Q=(-1,-1,3). Which of the following…

A: Which of the following points also lies in P