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

Q: a) Find the divergence and the curl of the vector field F × G, where F(x, y, z) = 2x²yi – y³z²j –…

A: Given information: Fx,y,z=2x2yi⏜-y3z2j⏜-2z2k⏜ Gx,y,z=3xyi⏜-5yzj⏜+z2k⏜ The vector field F×G can be…

Q: Find the divergence of the field. F = (2x+7y-8z)i + (5x +3y+6z)j + (-6x-y+2z)H div F =

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Q: Find the divergence of the vector field F at the given point. F(x, y, z) = xyzi + xz2j + 4yz²k; (5,…

A: Recall divergence is a scalar and has formula enclosed in next page

Q: What is the divergence of the vector field f=3x i+5xy j+xyz'k at the point (1, 2, 3). Select one: а.…

A: Solution:-The given vector  field is Step:-1    f=3x2i+5xy2j∧+xyz2k∧  then,  we have  to find the…

Q: 41.) Use given grid to sketch the vector field F = (y, -x). Include vectors at all integers points…

A: Given vector field is F=12y,-x

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: What is the divergence of the vector field f = x²i+ xyzj – zk at the point (1, 2, 3). Select one: а.…

A: f=x2i+xyz j-zK at (1,2,3)  div f=i ∂f∂x+j.∂f∂y+K.∂f∂z

Q: Calculate the divergence of the vector field F=x²y³z¹i-xyzj+(x+y+z) k

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Q: The divergence of a vector field F(x,y, z) = (x + y)i+ (y + z*)j + (x + z“)k at the point (1,1, 1)…

A: The divergence of a vector field is a scalar quantity that can be computed by computing the dot…

Q: 3) Sketch the vector field F. F(1, y, 2) = yi

A: F(x,y,z)=yi

Q: 2) Find the divergence of the vector field F(r, y, z) = (re") i + (ye") j+ (ryz) k %3D

A: We have to find divergence

Q: Find the divergence of the vector field F→(x,y,z)=xyzi→−yzj→+xzk→at the point (8,3,2) .   Enter…

A: The given vector field is : Fx,y,z=xyzi-yzj+xzk To find the divergence at 8,3,2

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: 10. Evaluate the divergence of the following vector field at the point (0,1,2): F = (xyz, x? + y? +…

A: Given: F=xyz,x2+y2+z2, xy+yz+xz       The point 0,1,2 To find the divergence

Q: Find the divergence of the vector field F = div F =

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Q: 3. Find the divergence of the vector field. F = ye2* i+2 ye³j 2.x²

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Q: a) Find the curl and the divergence of the vector field: F = (3x + 2z?)i + (*)j- (2- 7x)R.

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Q: Make a sketch of the following vector field. F = (-x,2y) %3D

A: We sketch the vector field, we choose  the  points and sketch them.

Q: Find the divergence of the vector field F = div F

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Q: 5. Suppose that the vector field F = is conservative. Find a potential function of the vector field…

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Q: 3. Let F be the vector field (ze²z + yz², xz², xe*z + 2xyz)

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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: 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: 4y V16+16g Find the divergence of the vector field F(z, 9) i+ V16z + 16g Provide your answer below

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Q: Q4. A vector field F is defined as F = psin pa,+ 2p² zas + zcos oa,. The V × F at point P(1, 7/2, 2)…

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

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Q: 9) Find the (i) divergence and (ii) curl of the vector field F(2, y, 2) = (4yz) i+ (y²z) j + (ryz) k

A: We have to find curl

Q: Find the divergence of the vector field F. F(x, y) = 4x²i + 5y²j

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Q: Find the divergence of the vector field. V(x, y, z) = 7e*Yj – 9e*Yj + 8EY²K - div(V) II

A: A detailed solution is given below.

Q: Find the divergence of the vector field F div F =

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Q: Find the divergence of the vector field F. F(x, y, z) = In( 7x²+ 4y² )i + 28xyj + In( 4y2 + 5z2 )k

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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: 9. (~Ch16 Review #13) Find the work done by the conservative vector field F(x, y) = along the curve…

A: given a conservative vector field  Fx,y=4x3y2-2xy3,2x4y-3x2y2+4y3 and a curve  rt=t+sinπt,2t+cosπt…

Q: 7. Choose an option in which the vector field is conservative: None of them OF = (xy, x+ y) O 2,…

A: A vector field F=∇f is conservative if and only if ∂M∂y=∂N∂x

Q: 2. Find the divergence of the vector field F div F = %3D

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Q: 5. Show that there is no vector field G such that: V x G = 2xi + 3yzj – xz?k.

A: Given that ∇×G→=2xi^+3yzj^−xz2k^. We have to show that there is no vector field G→ such that…

Q: Find the divergence of the vector field F. F(x, y) = 5x2i + 5y²j

A: The given vector field is: F(x,y)=5x2i+5y2j Let, F(x,y)=F1i+F2j⇒F1=5x2, F2=5y2

Q: 13. Calculate the divergence of the vector field F = x1e1 + 2x1e2 + +nx1en. ...

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Q: 3. Use the divergence of the vector field to compute F(x, y) = (tan-1 (2x)) ₁ + (xy-2 +²8²) J j 4 fo…

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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: Which of the following functions is a potential function for the conservative vector field F (x, y,…

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Q: Evaluate the divergence of the following vector field at the point (1,1,1): F= . Select one: O 5 1 3…

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Q: Evaluate F•Tds for the vector field F = x²i- yj along the curve x= y? from (1,1) to (4, – 2).

A: Answer = 19.5

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

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Q: Q5: Find the divergence of the vector field y F(x, y, z) = x² √yi + =j+zk At the point (2,4,1).

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Q: #7: Consider the following vector field. F(x, y, z) = 3yz In xi + (9x – 6yz)j + xy°z³ k %3D (a) Find…

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Q: Evaluate the divergence of the following vector field at the point (1,1,1): F = . Select one: 3 7…

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Q: ermine whether the vector field F(x, y, z) = (x³, 3zy², y³) is conservative on R³. If so, find a…

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