Find the curl of the vector field F. F(x, y, x) = 2yz'i + 3xj +&xk O 15r4 O 15:3 O (8yz – 8]j + (6xy-24)k O 8yz + 6xy-24-8

Q: c) Show that the vector field W(x, y, z) = (2yz+ xz – x², –2xz – yz + y?, y² – x² + z²) - - is a…

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Q: Calculate grad div F+ curl F at P(-1, 1, 1) where − = (3xz²)i + (xy)j + (2yz)k. O 7i+ 4j - 3k D-3i -…

A: we will find the required.

Q: 1) Find the work done by the vector field F(x, y, z) = (x², 4xy³, xy²) on a particle that %3D…

A: Given force is F→x,y,z=x2,4xy3,xy2 Let r→=rt→ be the boundary of the rectangle with vertices  0,0,0,…

Q: F = (x² +y², y² +z?,.

A: on solving this we get 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: Q4: Find the curl of the vector field F(x, y.2) = x*/yi +j+ zk at the point(2,4).

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Q: Sketch the vector field. У x F(x, y) = ( - 1/2, 2/2 ) x У 20 0 2 -20 0 -2 2 2 -2 2 -2 -2 2 -2 4 3 3…

A: Step 1:

Q: Determine the vector field of F. F(x, y) 3D yi — хј

A: Let us make a table to draw the vector field as shown in the image below.

Q: Find the Curl of the vector field. F(x,y, z) = 7e" sin(yi+ 8e* cos(y j+ 14z k a. &e" cos(y) +7e"…

A: solution of the given problem is below...

Q: Find the Curl of the vector field. F(x,y, 2) = 1le sin y i+ 12e* cos(y j+3z k a. (12e* cos(y) +1le"…

A: Curl of a vector can be calculated by forming a matrix and then finding the determinant of the…

Q: Compute the curl of the vector field F = sin(x) i+ cos(y) j+ 8z3 k

A:

Q: d) An open surface F is given by F = {(x,y, z) |z = 4 – x² – y² , z > 0} . Compute the flux of V…

A: V(x,y,z) = <2x+3y,2y+3x,-4z>F={ (x,y,z) : z=4-x2-y2 , z≥0}Consider, g(x,y,z) = z+x2+y2-4…

Q: Evaluate the 1-form φ = x2yz dx − z dy on the vector field V (x, y, z) = xU1(x, y, z) − yzU2(x, y,…

A: We need to evaluate the 1-form of  ϕ=x2yz dx - z dy.....(1) in the vector field  V(x,y,z) = x…

Q: Find the curl of the vector field F = curl F = i + 3 12 רז k

A: Step 1:

Q: Let C₁ be the line segment from the point (-4, 8) to the point (2, -4), C₂ be the arc on the…

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Q: Let F be the vector field (-2 sin(2x - y), sin(2x - y)). Find two non-closed curves C₁ and C₂ such…

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Q: Q5) If the vector field T = (axy + Bz³)a, + (3x² – yz)a, + (3xz² – y)a, is irrotational, determine…

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Q: Consider the given vector field. 8 x² + y² + z² (a) Find the curl of the vector field. curl F = F(x,…

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Q: What is the curl of the vector field F(z, y, z) = ryi+ zyzj + yzk O a. (-ry + z)i + (yz – 2)k O b.…

A: We have to find

Q: Show that the vector field F(x, y, z) = (-4y cos(4x), 4x sin(–4y), 0) is not a gradient vector field…

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Q: Let h be the vector field h(x, y, z) = (2xy + ²)i + (x² − 2yz)j + (2x= − y²) k. (a) Show that h is a…

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Q: Find the Curl of the vector field. F(x,y, 2) = 3e" sin(y)i+ 7e* cos(y)j+ &z k cos (y)i+ &z k. %3D…

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Q: 6 Find the curl of the vector field F = < yx³, xz5, zy curl F= + S k

A: Step 1: Step 2:Step 3: Step 4: