Suppose S is the surface where x² + y² + 3z² = 1. Let F be the vector field F = (xy, yz, z²). Evaluate fs(V × F) - dS. %3D

Q: Show that the vector field F(x, y, z) = xz i + xyz j - y 2 k can’t be written as the curl of another…

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Q: Sketch a sample of vectors for the vector field F(x, y) = (4x,y) Choose the correct answer below. O…

A: Make a table by considering some points and form from and to points as shown in step 2. Then plot…

Q: Consider the vector field F = (2y +1,y, –2²) along with the paraboloid surface z = r² + y. Find the…

A: Circulation is the line integral of the vector field along the curve

Q: Suppose the field lines of a gradient field F: R2 + R² are hyperbolas and the length of each vector…

A: To find- Suppose the field lines of a gradient field F : ℝ2 → ℝ2 are hyperbolas and the length of…

Q: Find the curl of the vector field F. F(x, y, z) = (2y - z)i + e²j + xyzk

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Q: Find all points (a, b, c) on the sphere x2 + y2 + z2 = R2 where the vector field F = yz2i + xz2j +…

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Q: Suppose S is the surface where x? + y? + 3z² = 1. Let F be the vector field F = (xy, yz, z?).…

A: suppose S is the surface where x2+y2+3z2=1 let F be the vector field Fxy, yz , z2 claim- evaluate…

Q: Find the flux out of the unit shpere for the vector field F(2,4, ;) = 1ā+3+K). %3D r answer =

A: Flux of F through the closed surface S is ∫∫sF→·n→dsS is the unit sphere x2+y2+z2=1Letϕ:…

Q: 10. For a vector field F = <2xy + y³, x² + 3xy²+ 2y7 find a function f such that F = Vr.

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Q: Find the curl of the vector field F. F(x, y, z) = 4x² + 7y²j + 5x²k

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Q: Consider the vector field F(x, Y, z) = 2xi + 2yj + 2zk. (a) Please compute V × F.

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Q: From the given vector field F⃗ (x, y, z) = , compute the curl of F⃗ and find the values of a and b…

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Q: What is the value of a so that the vector field F(x.y)=(In y+2xy³) i+(ax²y2+ x/y) j is conservative?…

A: To find: the value of a for which given vector field is conservative.

Q: Show that Gauss's Theorem holds for the vector field F(x, y)=(xy2, -yx2) in a side square 3.

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Q: Find the divergence of the vector field F. F(x, y, z) = In(9x2+ 6y² )i + 54xyj + In (6y? + 5z?)«…

A: To find the divergence of given vector field

Q: Question attached thanks!

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Q: Show that the vector field F (x, y, z) = xz i + xyz j y 2 k is not conservative.

A: Consider the following vector: Fx,y,z=xzi^+xyzj^+y2k^ Find the Curl of F→:…

Q: 13

A: We have to find out conservative or not

Q: Compute the curl of the vector field F = (xy+ z² ,x², xz – 2). curl(F(x, y, z)) =

A: Please refer the attached image for complete solution.

Q: Determine if the vector field is conservative. 1 -) (yi + «j) F(x,y) = 1+ xy, conservative not…

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Q: Compute the curl, Vx F, of the vector field. F(x, y, z) = 5xi + 3yj + 4zk %3D curl(F) =

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Q: Зу 1. Given the vector field F(x, y, z) = î+ Vrz j+x cos y - k, find curl F and div F.

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Q: Let ryz , (교2 + y"), 17 F = ( x2 +y? be a vector field on U = {(x, y, z) E R³ | (x, y) # (0, 0)}.…

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Q: Let Σ be the sphere x2`y2`z2 “ 25 with outward orientation and let F~ be a vector field with divF~ “…

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Q: Find the divergence of the vector field F. F(x, y, 2) = In(9x+ 8y² )i + 72xyj + In(8y² + 5z? )k #6…

A: Solution is done in step 2 and 3

Q: Verify Stoke's Theorem for the vector field F = (2y + 2) i + (x –2)ĵ+(y – x) . over the portion of…

A: The formula for stokes theorem is, ∫Pdx+Qdy+Rdz=∬∇×F.ndS Given that, F=(2y+z)i+(x-z)j+(y-x)k Then,…

Q: Consider the vector field F = 2xy i + (x2 + 2y) j. Verify the Green's Theorem in the closed region…

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Q: Find the divergence of the vector field F = < ya", xz°, zy* div F

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Q: For the vector field in three-dimensional space F = (4x°y – sin(x – 2))i+ e² v#j– yzk Evaluate…

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Q: Show that the following vector field is conservative and find the potential F(r, y, z) = (2ry, x² +…

A: The answer is given as follows.

Q: Find the divergence of the vector field F. F(x, Y, z) = In( 9x²+ 8y² )i + 72xyj + In(8y² + 7z? )«…

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Q: Compute the line integral of the vector field F = (4y, –4r) over the circle z2 + y? = 16 oriented…

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Q: Is the vector field F = [yze"yz, xze#yz, xye"yz] conservative? %3D O Yes O No

A: The vector field is conservative if ∇×F→=0 therefore, find ∇×F→ ∇×F→=ijk∂∂x∂∂y∂∂zyzexyzxzexyzxyexyz

Q: F=cos(x) î+sin(y) ĵ+cos (z) k

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Q: Consider the vector field F(x, y, 2) = (–7yz, 9xz, –5xy). Find the divergence and curl of F. div(F)…

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Q: Let be the vector field defined on the plane by F(x, y) = (x¹+3y, 6x - siny).

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Q: ) Show that the vector field, F3 yz £ + zx ŷ + xy 2 c

A: Given: The vector field is, F3 = yz x^ + zx y^ + xy z^

Q: Sketch a sample of vectors for the vector field F(x, y) = (3x y) Choose the correct answer below.…

A: The solution are next step

Q: Show that the vector field F = 2.xyi +(x² – 2 y)j is conservative and evaluate the line integral…

A: Given the vector field

Q: Show that the vector field F(x, Y, z) = (x² + y²)i – 2xyj is not conservative on R³.

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Q: Consider the vector field F(x,y,z)=(−3x^2,8(x+y)^2,9(x+y+z)^2). Find the divergence and curl of FF.…

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Q: Consider the vector field F = 2xy i + (x² + 2y) j. Verify the Green's Theorem in the closed region…

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Q: Evaluate the integral line of vector field F(x,y) -2y + 2x, 2²+ (y²/4) 2.x F(x, y) = + xy + 1 2² +…

A: Given Fx,y=-2yx2+y24+2x,2xx2+y24+xy+1We need to evaluate the line integral over C:x2+y2=1 oriented…

Q: the vector field F is shown in the xy plane. y 21 2 Is div F positive, negative, or zero? Positive…

A: Given : The vector field F is shown in the xy plane :   We have to determine that : Is div F…

Q: Determine whether or not F is a conservative vector field. F(x, y) = (my + ²)i + (mx + 7);

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Q: Use Gauss's Theorem to evaluate fF.ds for the vector field, F = x³ į+ y³ į+z³k, taking S S to be a…

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Q: If f(x,y) = x^3+y^3, sketch the gradient vector field: \grad{ f(x,y) }

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Q: Show that on the saddle surface z= xy the two vector fields (Vī+x² ± i+ y°, yvī+x² ±xvI+y°) are…

A: Let f(x,y,z)=xy−zf(x,y,z)=xy−z , (a,b,c)∈the saddle surface, and calculate the total derivative…

Q: Compute Sc F.d3 for the vedor field in the Cylinder with out ward facing and the surface which…

A: It is given that F→=xi+yj+ezk and the surface is x2+y2=4,1≤z≤5