Find the divergence of the field F. yj - xk F= 1/2 +: 2 OA. 3/2 2 -X O B. 3/2 2 X -y OC. 3/2 O D. 0

Q: Let F be a field of characteristic not equal to 2. Let D1, D₂ € F, neither of which is a square in…

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Q: gral of the field F(x,y,z) = 7xi + 7yj + 7zk across the portion of the sphere x2 +y² +z? = a? in the…

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Q: Find the divergence of the vector field F = ā x7, if r = xi+yj+ zk and ā = 3 i+3j+9k, by first…

A: First of all we calculated the vector F by calculating the vector product of the vectors a and r.

Q: Show that F is a conservative vector field and use this fact to evaluate F. dr along the given curve…

A: Consider the given function. Fx,y=x2i+y2j The compare the form of the function with the general…

Q: Find the divergence of the field F. F = 8x 5 i + 3y 5 j + 2z 5 k   a) 65   b) 8x4 + 3y4 + 2z4…

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Q: Find the divergence of the field. F=(-x+8y - 3z)i+ (8x- 4y + 3z)j+ (- 4x- y- 3z)k

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Q: Find the divergence of the vector field F. F(x, y) = 3xe*i - 9x²y²j

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Q: find the divergence of the field F = sin (xy) i + cos (yz)j + tan (xz) k

A: Given vector field,  F = sin (xy) i + cos (yz)j + tan (xz) k We have to find the divergence of given…

Q: find the work done by each field along thepaths from (0, 0, 0) to (1, 1, 1) in Exercise 1.F = 2xy i…

A: Given: F=2xyi+j+x2k To Find: Find the work done by each field along the paths from 0,0,0 to 1,1,1.…

Q: Determine the curl and divergence of F(XYZ) = xye* ^-x³yze²^ + + xy²e¹ k

A: To find- Determine the curl and divergence of Fx, y, z = xyex i^ - x3yzez j^ + xy2ey k^.

Q: Find the divergence of the vector field F. F(x, y) = 4xe*i - 7x?y²j

A: Find the divergence of the vector field F.

Q: find the divergence of the field. F = (x - y + z)i + (2x + y - z)j + (3x + 2y - 2z)k

A: Given Data The field function is fx=x-y+zi+2x+y-zj+3x+2y-2zk.   The expression for the divergence of…

Q: Find the divergence of the field. F= (4x + 5y + 7z)i + (8x - 8y + 3z)j + (2x - 7y + 4z)k div F =

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Q: (2) For a differentiable vector field f, which of the following is (are) incorrect? (a) ▼ × (▼ × ƒ)…

A: Since we know Formula a→×(b→×c→)=(a→·c→)b→-(a→·b→)c→

Q: Find the divergence of the vector field F = div F = %3D

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Q: Q3: Prove that the divergence of a curl is always zero.

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Q: Q4// A// Evaluate both side of divergence theorem for the field D=2xy.x^+x².y^ C/m2 and the…

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Q: Find the divergence of the vector field F. F(x, y) = 7xe*i - 4x²y²j

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Q: 3. Find a field F(x,y) = (M(x, y), N(x, y)) in the xy-plane with the property that at each point

A: Let f = xi + yj  Then F = ff = unit vector = xi+yjx2+y2

Q: EX2 : Find Divergence and Curl of the field function f j = In (x? + y?)i – 2z -tan + (5z + e' cos…

A: givenf→=ln(x2+y2)i-(2zxtan-1yx)j+(5z3+eycosz)kdefinition of Divergence…

Q: find the divergence of the field. F = (yexyz)i + (ze xyz)j + (xexyz)k

A: Given  F=(yexyz)i→+(zexyz)j→+(xexyz)k→ To find the divergence of the field If F=Pi→+Qj→+Rk→, the…

Q: Evaluate the Laplace Transform of: f(t) = 5e-at sin wt %3D OF(s) = O F(s) g2 –2as+s2+w2 O F(s) =…

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Q: Find the circulation of the field F = yi + (x + 2y)j around each of the following closed paths. a.…

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Q: find the divergence of the field. 1. F = (x - y + z)i + (2x + y - z)j + (3x + 2y - 2z)k 2. F = (x ln…

A: Consider the vector field Substitute the value of vector fields then Hence, the divergence of…

Q: Let F = (y cos 2x)i+(y sin 2x)j+(x²y+z)k. Is there a vector field A such that F = Vx A? ..... Select…

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Q: Find the divergence of the field F. F = 8x 5 i + 3y 5 j + 2z 5 k 8x4 + 3y4 + 2z4 O 40x4 + 15y4 +…

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Q: Given the vector field: F = (ry², y² + za", sin(x2)) (a) Find the curl of the field. (b) Find the…

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Q: Find the divergence of the vector field F. F(x, y) = 7XEX¡ – 9x²y2j

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Q: Is the following field path-independent/conservative? Cos(xy)i+ cos(ry) i F(x, y) 5xy 2 - No Yes

A: The given field is of the form Fx,y=Pi+Qj. Here P=5xy-cosxyx,Q=5x22-cosxyx.

Q: 3. Find the Laplace transform of f (t) defined by: f(t) = 0, for ! < 0 ? sinot, for t 2 0 %3D

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Q: Find the potential function f for the field F. F= i- k o f(x, y, z) = - 2 + c 2x o f(x, y, z) = - 2y…

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Q: Find the divergence of the following vector field: 00 O 2z O F = (y, -x + z², 3x)

A: We can solve this as follows:

Q: Find the divergence of the field. F = (- 6x + 8y – 4z)i + (- 8x – 5y + 3z)j+ (x + 5y + 2z)k div F =

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Q: Find the divergence of the following vector field. (x.y.z) F= 6+ 4x + 3y 2 The divergence of F is

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Q: 16: Evaluate the divergence of the following vector field. * D=RaR + R?cosøa, + R³cos²Øa

A: The given vector filed is: D=RaR+R2cos ϕ aθ+R3cos2ϕaϕ

Q: Find the divergence of the following vector field. (x.y.z) F= 2 y 4 +x + 9y The divergence of F is

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Q: Find the divergence of the following vector field. F = (2x?yz, - 2xy²z, - xyz²) The divergence of F…

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Q: Find the divergence of the following vector field. (x,y,z) F= 9+ 3x? +y? The divergence of F is

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Q: 3. Determine whether F is a conservative vector field. If it is, find a function f such that F = Vf.…

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Q: Which of the following is the divergence of the vector field F=x,y,z)? none of these 3. -3

A: The correct option is 3rd option .i.e. 3 .

Q: (a) For any vector field F, the gradient of the divergence of F is always zero.

A: Since the gradient of divergence of F is given by

Q: Find the divergence of the field. F= 5z e 8xyz i+ 5x e 8xyzj + 5x e 8xyZk div F=O

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Q: find the divergence of the field. 1.F = ye^(xyz)i + ze^(xyz)j + xe^(xyz)k 2. F = sin (xy) i + cos…

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Q: EX2 : Find Divergence and Curl of the field function f j In (x? + y?)i-(# i + (5z3 + e' cos z)k tan

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Q: Obtain the circulation integral of the field F = (x+eªseny)î + (x + e* cosy) in the curve C defined…

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Q: Q5: a) Show that the vector field F = (x² - y² + x)i - (2xy + y)j, is irrational.

A: Given vector field is F→=x2-y2+xi^-2xy+yj^. To show: Vector field F→=x2-y2+xi^-2xy+yj^ is…

Q: The curl ofvector field V = 2xy î + (x² + z²) ĵ+2zy k is O and irrotational (xy 1 – 2xyz k ) and…

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Q: Define the followings. 1. curl F, the curl of the vector field F = Pi + Qj+ Rk. 2. div F, the…

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Q: Find the gradient field of the function f(x.y.z) = In 4x + 4y2 +z?. ..... The gradient field is Vf=…

A: Gradient of F is given by

Q: Let F be a field of characteristic not equal to 2. Let a, b E F such that b is not T CL If 1

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