4 If the vector filed F(x.y.z) is given as F(x, y, 2) = (-y e *)i– (xe*)j i. Compute the value of curl F(x.y.z). ii. Find a function p(x, y,2) such that Vo = F(x.y, 2). iii. Calculate the value of V. F(x. y, z) at the point (r,,0)

Q: Evaluate the line integral F· dr, where F(x, y, z) = 3xi – 2yj – 4zk and C is given by the vector…

A: Given that F→=3 xi→-3 yj→-4 zk→ r→=sin t i→+cos t j→+t k→ and t is varying from 0→ 3π4  then x=sin…

Q: 1. Compute the vector line integral x dy + y² dx, where C is the part C of the curve y = p³ from (0,…

A: We need to find vector line integral.

Q: 4. Find the divergence and curl of the following vector function: F(x,y, z) = ( arctan(ry),…

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Q: The given vector function is F(x, y, z) = (2x – y + In(z² + 1))î + (x – 6e²y + 4 cos 4y)ĵ + | 2xz -…

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Q: Find the gradient vector field of f(x, y, z) = 9x5 + 7y3 + 6z?

A: To find the gradient of  f(x,y,z)=9x⁵+7y³+6z²

Q: 4. Is the vector field F(r, y, :) = (yz,rz, ry) conservative? Justify your answer.

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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: Consider the vector field F = (2y +1,y, –2²) along with the paraboloid surface z = r² + y. Find the…

A: Circulation is the line integral of the vector field along the curve

Q: Find the curl of the vector field F. F(x, y, z) = (2y - z)i + e²j + xyzk

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Q: Find the work done by the force field F on a particle moving along the given path. F(x, y, z) = yzi…

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Q: Suppose S is the surface where x? + y? + 3z² = 1. Let F be the vector field F = (xy, yz, z?).…

A: suppose S is the surface where x2+y2+3z2=1 let F be the vector field Fxy, yz , z2 claim- evaluate…

Q: From the given vector field F⃗ (x, y, z) = , compute the curl of F⃗ and find the values of a and b…

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Q: b) Given the vector field SUTM F(r, y, 2) = 3z cos ri+rlnyj+e* tan rk. Determine UTM i. div F, ii.…

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Q: Integrate the vector field over the curve C. F (x,y) =(y+1, 2x) C: x=4t, y=t², 0<t<1

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Q: Compute the line integral of the vector field F=⟨3zy-1 ,4x,−y⟩ over the path c(t)=(et,et,t)for…

A: To Compute the line integral of the vector field F=⟨3zy-1 ,4x,−y⟩ over the path c(t)=(et,et,t)for…

Q: Find the divergence and the curl of the vector field F(x, y, z) = x²yi + 2y'zj+3zk

A: The vector field given is : F(x,y,z) = x2y i +2y3z j + 3z k

Q: Consider the vector field: F(x, y, z) Show that F is not Conservative, i.e., not a gradient. sin…

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Q: Determine if the vector field F=(yz,xz,xy) is conservative?

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Q: How much work is required to move an object in vector force field F = (yz, xy, xz) along path r (t)…

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Q: Show that the vector field F (x, y, z) = xz i + xyz j y 2 k is not conservative.

A: Consider the following vector: Fx,y,z=xzi^+xyzj^+y2k^ Find the Curl of F→:…

Q: b) Find the flux of the vector field F(x,y,z) = 3xi – yj + 2zk; across o where o is the portion of…

A: The given question belonging to the vector calculus  in which we have to find the value flux of the…

Q: Integrate the vector field h (x, y, =)=ry i+yz j+x k over r (1u) = ui+ j+k, -ןue-L1

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Q: Compute the line integral of the vector field F=⟨3zy−1,4x,−y⟩ over the path c(t)=(et,et,t)for −4≤t≤4…

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Q: Find the divergence of the vector field F→(x,y,z)=7sinxi→−cos(3y)j→+z^9k→.   Enter the exact…

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Q: Find the divergence of the vector field. V(x, y, z) = 4yzi + 6xzj + xyk div(V) =

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Q: Q1 Use Stokes theorem to compute the flux of the curl of a vector field F = (2x – y)ĩ – yz? j- y²zk…

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

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Q: 2. Find the flux of the vector field F(x,y,z) = xi + yj + 2zk across o, where o is the portion of…

A: The given problem is to find the flux of the given vector field over the given portion of cone…

Q: der the plane in R³ defined by ve a normal vector for this pla

A: Note: As per our guidelines we cannot author hand written solution. Introduction: The normal vector…

Q: need some help with this

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Q: Compute the vector line integral x³ dy+y² dx, where C is the part of the curve y = x³ from (0,0) to…

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Q: Show that the work done by a constant force field F = a i + b j + c k in moving a particle along any…

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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: Compute the line integral of the vector field F = (4y, –4r) over the circle z2 + y? = 16 oriented…

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Q: Is the vector field F = [yze"yz, xze#yz, xye"yz] conservative? %3D O Yes O No

A: The vector field is conservative if ∇×F→=0 therefore, find ∇×F→ ∇×F→=ijk∂∂x∂∂y∂∂zyzexyzxzexyzxyexyz

Q: 3. Find the flux of the vector field F(x,y,z) = xi+ yj + 2zk across o, where o is the portion of the…

A: Find your answer below

Q: Select the irrotational vector field. OAyz 1-2xz1 + xyz k OB. yz 7 + xz 7 + xz R OCZ7 + z? Î + yz R…

A: We will find out the required value.

Q: 2) Given that the total flux across the surface, S of the tetrahedron bounded by the planes x = 0, y…

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Q: Consider the line integral a xy dx + yz dy + xz dz. (a) What is the vector field that is being…

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Q: Show that the vector field F(x, Y, z) = (x² + y²)i – 2xyj is not conservative on R³.

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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: Calculate the divergence of curl of vector F = e22+y î + sin yz² j+ cos yzx k, V• (V × F).

A: NOTE: According to guideline answer of first question can be given, for other please ask in a…

Q: ƏF dF = (dr. V)F+ -dt. at

A: Given: A vector function F depends on both space coordinates x, y, z and time t.  To Find:  To show…

Q: Suppose a vector field F(r, y) = construct a potential function o(r, y). i+ j is conservative. Then

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Q: (a) Calculate the divergence of curl of vector F = e2z+y i + sin yz? j+ cos yzx k, V (V x F).

A: The given vector is F=e2x+yi+sinyz2j+cosyzxk To find the divergence of the curl of F .

Q: Which of the following vector functions represents the curve of intersection of the cylinder x2 + z2…

A: We have to find vector functions representing curve of intersection of cylinder and plane. Plane…

Q: Let, T:R' → R';T(x, y,z) = (x – y,2x + 3y + 2z,x+ y+2z) . verify that [T][v], = [T (v)]; for any…

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Q: Show that on the saddle surface z= xy the two vector fields (Vī+x² ± i+ y°, yvī+x² ±xvI+y°) are…

A: Let f(x,y,z)=xy−zf(x,y,z)=xy−z , (a,b,c)∈the saddle surface, and calculate the total derivative…

Q: Find the work done by the force field F(z,y,2) = Ir+v,rs, y+:) on a particle that moves along the…

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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.