9. Find the flux of the vector field B(x, y,=) shown in the left figure through the square S of - yỉ +xj side 2 shown in the right figure , oriented in the j direction, where B(x, y,z)= x+y? S 2 1

Q: 5. Find a potential function corresponding to the vector field F(r,y, 2) = (2r, 3y, 4:).

A:

Q: 8. Compute the flux of the vector field. F(x,y,z) = (2x -z,-2y, 1-2x) through S= {(x,y,z) € R³: z =…

A:

Q: 2.10 (a) Express the vector field H = xy'za, + x'yza, + xyz'a. in cylindrical and spherical…

A:

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: 9. Compute the flux of the vector field F(x, y) = (-x sin(1+xy) – 4 cos(TY), y sin(1+ xy) + 6x)…

A:

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: 8. Find the flux of F = (2x – 5y², 3y, x) out of the sphcre of radius 2 centered at the origin.

A: The flux of the vector space is given by the formula, ∫S∇.F dS where S is the sphere of radius 2…

Q: 1- Prove that the force field F known as : Prove that the force field defined by F = (y*z' -6xz? )i…

A:

Q: (b) Compute the flux of the vector field F(x, y, z) = y i– 2.xyk over the triangle T with vertices…

A: Given vector field is: F→=yi^-2xyk^ Given vertices of the triangle are: 1,0,0, 0,1,0 and 0,0,2 Then…

Q: Compute the flux of the vector field F(x, y, z) = 5i + 5j+ 6k through the rectangular region with…

A: Given that, The vector field F→x,y,z=5i→+5j→+6k→ through the rectangular region with corners at…

Q: Prove that F(x, y, z) = (y² cos x + 2*)i+ (2y sin x – 4)j+ (3xz2 + 2)k - is a conservative vector…

A:

Q: 1. Consider the vector field F(x, y, z) = (2e2" cos(3y), –3e²" sin(3y) + Y a. Find divF(x, y, z) and…

A:

Q: 5. Consider a parabolic solar panel which lies in the part of z = x2 + y? below the plane z = 1,…

A: Solution...

Q: Find the work done by the force field F in moving an object from P(-3, 7) to Q(7,5). 2x Y F(x, y) =

A: To find the work done by the force field F in moving an object from P-3, 7 to Q7, 5. Fx,…

Q: 5. Find the outward flux of the vector field F(x, y,z) = x²i + y°j+z²k through the first octant…

A:

Q: Consider again the vector field F = (x +y)i + (x² + y²)j_what is the downward flux across the line…

A:

Q: 5. Given the vector field F(x, y, 2) = (2x In y|+ 2°|2yz) find the following a. Gradient of . b.…

A: As per Bartleby guidelines, for more than three sub-parts asked for a question, only three is to be…

Q: Determine the value of k for which (u, v, w) is an orthogonal coordinate system if x = −(u2 + kv2),…

A: note : As per our company guidelines we are supposed to answer ?️only the first question. Kindly…

Q: b) Find the curl of the vector field, CurlF, if F= Axzi- By 2 j+ Cx z°I where the coefficients A, B,…

A: As per Bartleby guidelines for more than one questions asked only first should be answered. Please…

Q: Compute the flux of the vector field F(x, y, z) = 6ỉ +3j + 2k through the rectangular region with…

A:

Q: b) Find the curl of the vector field, CurlF, if F= Axzi- By 2j+ Cx tk, %3D where the coefficients A,…

A:

Q: 5) Find the work done by the force field F(r, y, z) = ri-zj+y k in moving an object along the…

A: Work = Force X Displacement

Q: 10. [ Find the flux of the vector field F(x, y, z)= 3 over the surface S, where S is the surface of…

A: The general form of a vector-valued function in three dimensions is given by F→=Fx, Fy, Fz, where…

Q: 3 2) Integrarte the vector field hlxry,2)= xyi + ya J+xa k over the twisted cubic PIt)=ti+t?g + t3 k…

A: Given that, the vector field        h(x, y, z) = xy i + yz j + xz k        r(t) = t i + t2 j + t3 k…

Q: Calculate the flux of the vector field (x, y³), out of the annular region between the x? + y? = 1…

A:

Q: (c) Determine the flux of the vector field F = x³i – 2yĵ + 7z²k across a cone z = x2 + y2 + 3 that…

A:

Q: 5. Show that F =(y cos(x),sin(x)+ y) is a conservative vector field and use this to calculate the…

A: Given: F → = y cos(x), sin(x) + y. A vector field F→ = P, Q is said to be conservative if partial…

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

A:

Q: Calculate the flux of the vector field F = -2i + 5æ²j – 3k, through the square of side 2 in the…

A:

Q: 2. Letr =√x² + y² + z². (a) For n ≥ 1 and r> 0, express V(r-n) in terms of r and the radial vector…

A: Given  solution(a): Radial vector field  solution(b):

Q: 7) Consider the vector field F(x, y,z)= (y,z,x). Find the flux of this vector field across the…

A: Flux = double integral of (F(r(u,v)).ru*rv) dvdu

Q: Let F(x, y) = (4 cos(y), 2 sin(y)). Compute the flux $ F - n ds of F across the boundary of the…

A: By using Green Theorem, ∮F.n ds…

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: 3. Find the work of the vector field F(2, y, ) = yi along the curve which is obtained as the…

A: To find the work of the vector field Fx,y,z=yi along the curve obtained by the intersection of…

Q: Compute the flux of the vector field i = -2i+ j- 2 k through the rectangular region shown below,…

A:

Q: 2.4) Use the divergence theorem to find the outward flux of the vector field F(x, y, x) = x³i+ y³j+…

A: The divergence of the given vector field is  ∇·F=∂∂xx3+∂∂yy3+∂∂zz3=3x2+3y2+3z2 Let, S be the surface…

Q: 6. Compute ſ, F-·dr where f(x, y) = (y² cos x, 2y sin r) and C is the straight line path starting at…

A:

Q: Find the work done by the force field F in moving an object from P(-4, 8) to Q(6, 4). F(x,y) = 2* 1…

A:

Q: he temperature in a temperature-controlled chamber is given by a 3D scalar field Tlx, y, 2) = Ax®yz…

A: Note- Since you have asked multiple questions, we will solve the first question for you. If you want…

Q: Consider again the vector field F = (x + y)i + (x² + y² )j. What is the downward flux across the…

A:

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

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

Q: 16. Compute the flux V· nds of the vector field V(r, y) = (x² – 2ry, y² – 2xy) across the curve C :…

A: We have to compute the flux ∫ℂV·nds of the vector field Vx,y=x2-2xy,y2-2xy across the curve…

Q: 12. Find the flux of the field F(x, y, z) = 4xi + 4yj + 2k outward (away from z-axis) through the…

A: Flux of the given field is given by

Q: (a) Express the vector field D = (x² +y<)-1 (xax – yay) in cylindrical components and cylindrical…

A: Given vector field: D =x2+y2-1  xax-yay a) To express the vector field  in cylindrical components…

Q: 12. Find the flux of the field F(x, y, z) = 4xi + 4yj + 2k outward (away from z-axis) through the…

A:

Q: 7. Find the outward flux of the field F(x, y) = -yi + x²j across the closed counter-clockwise curve…

A: Consider the given field: F→(x,y)=-yi^+x2j^ and

Q: 5. Find a potential function corresponding to the vector field F(x, y, z) = (2x, 3Y, 4z).

A:

Q: Compute the flux of the vector field F = 2xi + 3yj through the cylindrical surface shown below, if a…

A: We have to compute the flux of the  given vector field.

Q: 4. Given the vector field Č = p² sin o a, + (z² cos – 1)as + (p² – z)a, Determine the x-component of…

A: Given the vector field