8) The vector field Vp[x, y] = F =- has a potential function p[x, y] = a) (x² + y²)³2 b) d) Vx? +y? e) F[X] has no potential function.

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: Is the vector field F = y? – 2x², 2xy + 3| conserva Yes No yz Is the vector field F y? – x2 con Vy?…

A: According to the guidelines issued by the company we are supposed to answer only first question.…

Q: 2. Given vector field F= (-2y, z-2x, y + z), find the work done by ♬ on a particle that moves along…

A:

Q: Let F be the vector field (-2 sin(2x - y), sin(2x - y)). Find two non-closed curves C₁ and C₂ such…

A:

Q: 1. Find a potential function for the vector fields a) b)

A: As per the company's guidelines, we are supposed to solve the first question for you, kindly repost…

Q: 1- a) c) −2ñi + (2ñ + 1)j b) 2πi + (2π − 1)j - 4пi – (2n + 1)j 2лi + (2π + 1)j 4ñi + (2ñ + 1)j Leave…

A: Given:The given function is .To Find:We have to determine the gradient vector of  at the point…

Q: Show that curl(F) = 0 and that, SF· dr = 27 where C is the circle of radius 1 centered at the origin…

A:

Q: a) Determine whether or not the vector field F 8yz, – 6 cos(y) – 8xz, – 8xy + 10z > - is…

A:

Q: h) Given vector field F (x, y, z) = (2x + 2y + 4z) i + (2y + 2x – 32) j + (2z – 3y + 4x) k. (a)…

A:

Q: 1) Given the vector fields F1 = x²2 and F2 = xâ+ yŷ + z2, calculate the divergence and curl of F1…

A:

Q: Given the vector field F(x,y,z) = (y²,2xy-e²¹) and the path C given by r(t) = cos(t)i + sin(t)];…

A:

Q: 9. Find the flux of the vector field B(x, y,=) shown in the left figure through the square S of - yỉ…

A: The general form of a vector valued function in three dimensions is given by…