Find all points (a, b, c) on the sphere x2 + y2 + z2 = R2 where the vector field F = yz2i + xz2j + 2xyzk is normal to the surface and F(a, b, c) ≠ 0.

Q: Compute the upward flux of the vector field Ĥ(x, y, z) = (x, 0, 2z) across the portion of the…

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Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi – 2xzj + yzk; (7, –9, 5)

A: Given vector field F(x,y,z) =x2 z i -2xz j +yz k   ; (7 , -9 , 5)

Q: Find the flux of the vector field F = (y, z, x) across the part of the plane z = 4+ x + 3y above the…

A: The surface integrals compute the flux of fields across surfaces,                   So,…

Q: Find the flux of the vector field V(x, y, z) = 3xy²i + 5x²yj + 2z³k out of the unit sphere. Flux =

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Q: Find llFll and sketch several representative vectors in the vector field.

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Q: F = (x² +y², y² +z?,.

A: on solving this we get the

Q: Find the outward flux of the vector field F = (x³, y³, z²) across the surface of the region that is…

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Q: Use the Divergence Theorem to compute the flux across the sphere x2+y2+z2 = 1 within the vector…

A: The answer is as follows:

Q: Compute the flux of the vector field F(x, y, z) = (2y, 3, –2xz) through the surface S, which is the…

A: Given vector field is, Fx,y,z=2y,3,-2xz. The given surface is, y=x2+z2  and  x2+z2≤1. Now for the…

Q: Find the curl for the vector field at the given point. F(x, y, z)= 6xyzi+6yj+6zk (6, 7, 6) O…

A: To find the curl for the vector field  at the given point.Fx, y, z=6xyzi+6yj+6zkPoint=6, 7, 6

Q: Find the work done by vector field F(x, y, z) = xi + yj + (x + z)k on a particle moving along a line…

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Q: Calculate the flux of the vector field F(x, y, z) = 5i + 2j+ zk through the closed circular cylinder…

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Q: : Find the divergence of the vector field At the point (2,4,1). F(x, y, z) = x² √yi+j+zk

A: We have to find the divergence of the vector field F(x, y, z)=x2y i^ +yxj^+zk^ at the point (2, 4,…

Q: Find the gradient vector field of f(r, y) = In(x + 3y)

A: Solve for the gradient vector

Q: Find the curl of the vector field at the given point. F(x, y, z) = x2zi – 2xzj + yzk; (9, -9, 5)

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Q: Consider the vector field F (x, y, z) = (y - zsinx, x, 2z + cosx). The work that performs the F…

A: Given that, F(x,y,z)=y-zsinx, x, 2z+cosxA body is displaced from point A(3π,-1,1) to point Bπ,2,0

Q: Find the curl for the vector field at the given point. F(x, y, z)= 6xyzi+6yj+6zk (6, 7, 6)

A: step 2 complete solution

Q: Find the flux of the vector field F = (y, – z, x) - 2, - across the part of the plane z = 2 + 3x +…

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Q: Determine the line integral if the vector field is F(x, y) = x²yî – 2xyf On a rectilinear path that…

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Q: Compute the flux of the vector field F(x, y, z) = 2xj+ 4yk through the surface S, where S is the…

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Q: Sketch a few representative vectors of vector field F = ⟨0, 1⟩along the line y = 2.

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Q: Compute the curl, V x F, of the vector field. F(x, y, z) = 7xi + 9yj + 2zk curl(F) = -7xi – 5yj +…

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Q: Find the flux of the vector field F = (y, - z, x) across the part of the plane z = 4+ 2x + 3y above…

A: The given vector field is, F→=y, -z,  x. The given part of the plane is z=4+2x+3y And the rectangle…

Q: for the vector field F = 2xz i+ (1 – 4xy² ) j led by the plane z = 6 – 2x² – 2y² and the plane

A: We have to find the following conditions according to the given information

Q: For the vector field F = ((y/z2+1)i + (-2x/z2+1)j + (3x2+3y2/(z2+1)2)k , calculate curlF

A: We have given vector field F=yz2+1i+1-2xz2j+3x2+3y2z2+12k=yz2+1,1-2xz2,3x2+3y2z2+12=F1,F2,F3…

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: Compute the flux of the vector field (x, (æ°, – ay*), out of the rectangle with vertices (0,0),…

A: To compute the flux of the vector field x3,-xy4, out of the rectanglewith vertices 0,0,2,0,2,4…

Q: Find the flux of the vector field F = (y, - a, z) through the helicoid with parameterization r(u, v)…

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Q: the gradient vector field of f(z, y) = In(x + 4y) %3D Work

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Q: Find the curl of the vector field F. F(x, Y, 2) = arcsin yi+ V1 - xzj + yêu y²k

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Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi – 2xzj + yzk; (7, -9, 5)…

A: Concept:

Q: Find the curl for the vector field at the given point. F(x, y, z)= 6xyzi+6yj+6zk (6, 7, 6) O…

A: We have to find the curl

Q: Find the level surfaces of the scalar field U = ear, where the vectors are: a = (2, 2, 1) and r = =…

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Q: disk

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Q: Find the flux of the vector field F = (y, – z, x) across the 2 + 4x + 3y above the rectangle part of…

A: “Since you have asked multiple question, we will solve the first question for you. If youwant any…

Q: Compute the flux of the vector field F(x,y, z) = yi– 2xyk over the triangle T with vertices (1,0,0),…

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Q: Compute the flux of the vector field F(x, y, z) = 3x + 3yk through the surface S, where S is the…

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Q: F=x²y³z¹i-xyzj+(x+y+z)k

A: The vector field is F→=x2y3z4i^-xyzj^+(x+y+z)k^

Q: Use the Divergence Theorem to find the flux of the vector field F = (3x2 – 3yz + 423) i + (4.xz –…

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Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi – 2xzj + yzk; (3, -9, 7)…

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Q: Show that the vector field F(x, y, 2) = (2x cos y – 3)i – (x² sin y + 2²)j – (2yz – 2)kis a…

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Q: xi + yj F(x, y) = k- x² + y2'

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Q: Calculate the flux of the vector field F 6i + 2x2j- 2k, through the square of side 4 in the plane y…

A: Given vector field is F→=6i→+2x2j→−2k→ We have to find the flux of the given vector field. The flux…

Q: The outward flux of the vector field F=(x,0, z) across the cylinder x + y = 1, for 0<z<1, is %3D…

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Q: Compute the flux of the vector field F(x,y,z)=5xj+2yk→through the surface S, where S is the part of…

A: Flux problem...

Q: If the vector field A = âx3x² + âyy – â̟5z³ is given, express à in cylindrical and spherical…

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Q: Sketch the vector field F(x, y) = (-x − y, x - y) at the points (x, y) where x, y = {−1,0,1}.

A: Consider the given vector field, F→x,y=-x-y,x-y Here we need to sketch the vector field at the point…

Q: Find the flux of the vector field (y, x, z) in the negative z direction through the part of the…

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Q: Find the curl of the vector field F. F(x, y, z) = arcsin yi + V1 - x2j + y2k

A: To find the curl of the given vector field F

Q: Find the flux of the vector field F(x, y, z) = [x4, −4yx3, 7z + sin(xey))] through the outwards…

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