The outward flux of the vector field F(x, y, z) = (x, y, z?) across the boundary of D = {(x, y, z) E R: -1 < z < -a2 – y?} is A) 3 В) 2т Gesture Mode С) 4т 日6

Q: Find the work done by a force F = 6ỉ + 5j– 3k when a particle moves from point P(-3, 4, 5) to point…

A:

Q: a) Find the values A and B that allow the vector field given below to be conserved. F(x,y,z)=2xlnz…

A: (a) Given vector field is Fx,y,z=2xlnz i+3Bz j+x2zA+y3k Now, F1=2xlnzF2=3Bz F3=x2zA+y3

Q: f is a potential function for the vector field F = (2x - 2yz, 3y2 - xz, -2xy) so what is the value…

A:

Q: Find curl(curlF→(x,y,z)) of the vector field F→(x,y,z)=x^9zi→−9x^8zj→+yzk→. Enter the exact answer.…

A:

Q: Determine whether →F(x,y,z)=3x^2yˆi−yzˆj+zx^2ˆk is a conservative vector field.     Component of…

A:

Q: Determine the flow of the vector field (image 1), through the surface S, outwards, with S being the…

A: Given :- The flow of the vector field through the surface S , outwards , with S  being the…

Q: What is the dimension of the vector space ab c S= { EM2x (R): a =b=c} de f

A:

Q: Evaluate :// F. d5 , where F = and S is the helicoid with vector equation r(u, v) upward…

A:

Q: Let f(x, y) = x^2/(x + y). Find a unit vector u such that Duf(1, 2) = 0

A: f(x, y) = x^2/(x + y)

Q: Let F and G be vector fields with differentiable components. Express curl (F × G) in term of div and…

A: Let F and G be vector fields with differentiable components.Let We will compute .The cross product…

Q: Find the divergence in (2,1,-1) for the vector field FCX₁Y₁² ) = x³y² 2 ² + x ² z 3 + x^²yk

A:

Q: (1 point) Show that the vector field F-yz Ч + zz 1 J-zuz 2 k is conservative by finding a scalar…

A: To find the scalar potential function f, assume

Q: Find the curl of the vector field F = curl F = i j+ ان اچ k

A:

Q: Solve using method of undetermined coefficients: y" + y' - 2y = x². %3D

A: Solution :-

Q: 5 Let fi R²→R be the vector field given by F (x,y)- (4,-x). A- Calculate the circulation of f when…

A:

Q: Which of these vector fields are irrotational? Identify all of those that satisfy this property. A B…

A: The given vector fields, A) u=-x, y, 0B) u=-y, x, 0C) u=-x, z, 0D) u=x, y, z We have to find the…

Q: Let f(x, y) = ln (1 + x² + y²), then a) f is not differentiable at (0, 0). b) Exists a point (xo,…

A: We are given the function fx, y=ln1+x2+y4. Our aim is to choose the correct option for the given…

Q: Find the area of the portion of the unit sphere inside the cylinder x2 + y? = 1/2 and z > 0. Select…

A:

Q: Find the potential function for the vector field given as 2 F(x.y.?) = Oa. $(x, y, z) =x*y + x²2?…

A: Answer:   The correct option is B.

Q: Let F = be a vector field in space Find the potential function f(x,y,z) of F

A:

Q: Let ryz , (교2 + y"), 17 F = ( x2 +y? be a vector field on U = {(x, y, z) E R³ | (x, y) # (0, 0)}.…

A:

Q: For the scalar function f, div(grad f) is equal to Select one: a. + + dx?' ay? ' az? b. dx dy dz C.…

A:

Q: 5) Find the work done by the force field F =-yzi+xz j +xy k as the point of application moves from…

A: Yes, the amount of work done in this case is independent of the path taken. This is because the…

Q: In a rectangle, the width is one-third the length. The total perimeter is 40 inches. Find the length…

A: Solution: Given:    Width is one third of the length of rectangle     and the perimeter of rectangle…

Q: 5) Given the vector field F(x,y,z) = (2x+ y)i + (x + 2yz³)j + 3y²z²k a) Check if the vector field is…

A: To check if F is conservative:Find curl F and if it equals to 0 then F is conservativeSo, it will…

Q: A vector field representing wind speeds is given by v = æy³ i + 3x³y³j. %3D A walker can take one of…

A:

Q: Determine the vector field of F. F(x, y) = 4i - 2j O O Y X X

A: