3) Evaluate curl(F F(x, y. =) = (y=+2xy, 2xy + x + =, xy + 23z) to show that is conservative.

Q: Q2. If F = (x² - y² + 2xz)ī− (2xz − xy + yz)j + (z² + x²), find the divergence of curl F and curl of…

A:

Q: Find the curl of the vector field F (5x sin(y), 2y cos(æ)) curl F =

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Q: Compute the curl of the following vector field. F = = (3z2 sin y, 3xz2 cos y, 6xz sin y)

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Q: npute the curl of the vector field F = (y – 5æ) i+ (5y + 2) j+ (x – 52) k

A: Solution of the problem as follows

Q: calculate div(F) and curl(F).  F = (x, y, z}

A: Answer(a): div(F)=3

Q: Find the directional derivative of the field f(x, y, z) = In(4 x) at P = (1, –2, –5) in the…

A:

Q: Find the gradient vector field of f(x, y) = ln(5x + y)

A:

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

A: Solve for the gradient vector

Q: 2. Find the curl of the vector field. F = z°e* sin(2 y)i – e' cos yj+ xyzk to

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Q: Find the curl, the divergence and the potential (if it exists) of F = (2x + y², 2ry + 3y²z*, 4y°z³)

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Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = ln(x + 5y + 6z). F(x, y, z) = =

A:

Q: Δ denotes the Laplace operator defined by Δφ = ∂2φ/∂x2 + ∂2φ/∂y2 + ∂2φ/∂z2 . Show that if F is the…

A: A function ux,y is called harmonic if it is twice continuously differentiable and satisfies the…

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = tan(6r + 2y + 2) . F(2, y, 2) =

A: Find the gradient vector field

Q: Find the work done between point 1 and point 2 for the conservative field F. F= (y +z)i + xj + xk;…

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Q: Find the curl of the vector field F = (3y cos(x), 6x sin(y)) curl F = %3D

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Q: Let f(x,y, z) = xy – yz and v [2y, 2z, 3x]. Find Curl(fv).

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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: Find the gradient field of the function, g(x,y,z) = e 3z - In (x +2y).

A: Given function  gx,y,z=e3z-lnx2+2y2                     (1) The gradient field is  ∇g=∂g∂x,∂g∂y,∂g∂z…

Q: Is there a vector field G on R³ such that curl G = (x sin y, cos y, z - xy)? Explain

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

A:

Q: Find the gradient vector field of f(x, y) = tan(2x − 3y).

A: Given fx,y =tan2x-3y         we find the gradient vector of fx,y

Q: If F(x, y, z)= xz i  + xyz j - y 2 k find curl F

A: given: F(x,y,z)=xzi+xyzj-y2k we have to find the curl F. as we know that if we have F→=Fxi+Fyj+Fzk…

Q: The curl of f(x,y,z)=xyzj is =.

A:

Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = In(4x + y + 62) . F(1, y, 2) =

A: we have to find the gradient vector field of f

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: ind the curl and divergence of F(x, y, z) = (e², –2ev², 3xe").

A:

Q: Find the gradient field associated with the function φ(x, y, z) = xyz.

A: To find the gradient field associated with the function  φ(x, y, z) = xyz.

Q: If F = xyz i+ zxj +xy'z k then find curl F at (1, 2, – 1).

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Q: Find the curl of the vector field F = (4x sin(y), 7y cos(x)). curl F - Dretieur

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Q: Let F1 = (x+ y)Âx + (-x+y) ŷ– 2zî and F2 = 2 yx+ (2x +3z) ŷ +3yî. Calculate the curl and divergence…

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Q: Find the curl of the vector field F = (6y cos(x), 7x sin(y)) curl F =

A: If  F=f1x,y, f2x,y   thenCurl F=0,0,∂f2∂x-∂f1∂y

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

A:

Q: Find the curl of the vector field F = (3y cos(x), 5x sin(y))

A:

Q: Find the curl of the vector field F = (3x sin(y), 7y cos(x)).

A: The solution is:

Q: Find the curl of Ū = e*yax + sin(xy) a, + cos²(xz) az. 2z cos(xz) sin(xz) ay + [x cos(xy) – ye*y]a,…

A:

Q: (3)If F = (x points (2,1,1) ² yz, xyz² , zy² ). Find curl curl F at

A:

Q: Find g(x, z) so that F(x, y,z) = (8x cos y sin? z + 2e2xz)î – (4x² sin y sin? z)j+ (g(x, z) cos y +…

A: Given that    Fx,y,z=8x cosy sin2z+2e2xz i^-4x2 siny sin2z j^+gx,zcosy+2e2xz k^ Now we have to find…

Q: F=cos(x) î+sin(y) ĵ+cos (z) k

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Q: a) let F = (y+2)i +(z+x)j+(x+y)k %3D find a) Curl F b) Diverynce of

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Q: If F = (x² − y² + 2xz)i + (xz − xy + yz)j + (z² + x²)k, find the divergence of - curl F and curl of…

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Q: Compute the gradient field of f(x, y, z)= e^z + xy^2

A: Take gradient to solve

Q: What is the largest possible magnitude of Curl(F) where F(x, y, z) = (4, a/9 – y?, 6z)? у, х

A: Given that F→x,y,z=4,x9-y2,6z

Q: Find the directional derivative of the field f(x, y, z) = -4x³ + 3 xy² + 5 y³ at P = (-1,–3,5) in…

A: Given f(x,y,z)=-4x3+3xy2+5y3  we have to find directional derivative of f at P=-1,-3,5 in the…

Q: Find the curl of the vector field F = (3y cos(x), 4x sin(y)). curl F = %3D

A:

Q: Find the gradient vector field (F(r, y, z)) of f(x, y, z) = z sin(ry). F(2, y, z) = (

A: Given function is  f(x,y,z) = z^2 sin(xy)

Q: Find the gradient vector field (F(r, y, z)) of f(x, y, z) = x² sin(3yz) F(z, y, 2) = (

A:

Q: Find the gradient vector field of f. 5y f(x, y, z) = x cos %3D Vf(x, y, z) =

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Q: Compute the curl of the vector field F = 2y3 i+ e j+ cos(x) k curl

A:

Q: (1) Find the curl of the curve F=(x*y.y*z.2x) (0.0. y+1) (-x'.2'.y+1) b) d)

A: We have to find the curl of the curve F=(x2y,y2z,z2x) curl is defined as the cross product of ∇ with…

Q: B) Find the work done by the conservative vector field F (x, y, z) = yzi+xzj+xyk along a smooth…

A: Since, it is given that the field is conservative.

Unitary Method

The word “unitary” comes from the word “unit”, which means a single and complete entity. In this method, we find the value of a unit product from the given number of products, and then we solve for the other number of products. 

Speed, Time, and Distance

Imagine you and 3 of your friends are planning to go to the playground at 6 in the evening. Your house is one mile away from the playground and one of your friends named Jim must start at 5 pm to reach the playground by walk. The other two friends are 3 miles away.

Profit and Loss

The amount earned or lost on the sale of one or more items is referred to as the profit or loss on that item.

Units and Measurements

Measurements and comparisons are the foundation of science and engineering. We, therefore, need rules that tell us how things are measured and compared. For these measurements and comparisons, we perform certain experiments, and we will need the experiments to set up the devices.