Let F (x, y, z) = (e*y - 2x, ex + 2yz, e*xy + y?). a) Using the Curl-test decide whether F is conservative or not! If it is, determine the potential function! b) Let y be the broken line connecting the points A = (1,-2, 0), B = (0, 2, 2) and C = (0, 1,0). Calculate F dr =? %3D

Q: calculate the curl and Divergence A= xyzi-2r2lny +2yak at リ-ル1).

A: Given: A=xyz3 i-2x2z ln y j+2yz4 k              point is (1, -1, 1)∇.A=∂ ∂xi+∂ ∂yj+∂ ∂zkxyz3 i-2x2z…

Q: 4. Find the flux of F across S if F = yi-xj+2zk and S is the hemisphere x² + y² + z² = 4, z ≥ 0,…

A: We have to find flux passing through sphere.

Q: Consider the vector function F(x, y, z) = x²y² z+ 5xz xz2 -> y3/27 - - -k 4 and calculate the…

A: The divergence of the given vector field is:  2xy2z−2y25​15xz​−2xz​ In case of doubts please do let…

Q: Find div(curl F) = V. (V x F). F(x, y, z)= xyzi + yj + zk

A: If vector field then from the question

Q: 49. Let f(x, y, z)=sin(x² + y² +2²). (a) Describe in words the shape of the level surfaces of f. (b)…

A:

Q: Explain why that in a classroom of 30 people, at least two of them must have last names that start…

A: We have to explain why that in a classroom of 30 people, at least two of them must have last names…

Q: Let flxiy) = Rx Jy 27 %3D a) Finid the gradrent of f b) Find the directional derivative of f at the…

A: Consider the function as  fx,y=2xy

Q: Find the gradient vector field of f(x, y, z) = x³y* + y° z³ + xz°.

A:

Q: Q3A) Find normal line and parallel plane to the function f(x, y, z) = x²y²z² - 4 At point (1,-1,2).

A:

Q: Let F = = (x, y, z) (x² + y² + z²)3/2 Use the fact that V F = 0 when (x, y, z) following surfaces.…

A: Step 1:- To find the flux of the vector field F=(x2+y2+z2)3/2(x,y,z)​ through the given square…

Q: Find the Jacobian w/ respect to UVW X=U(3-v), Y= uv(3-w), Z=Uw

A: Our aim is to find the jacobian of x=u(3-v), y=uv(3-w) and z=uvw⇒x=3u-uv ,   y=3uv-uvw and…

Q: Let F(x, y) = (e, e-). Determine the integral curves for the vector field.

A: Given vector field F(x,y)=ex, e-xWe need to find the integral curve.

Q: Find the work F dr done by the force field F = (y, x, z) on a particle that moves along C the line…

A:

Q: EXERCISE 2 Consider f(x, y) = 3x² – 4y² and = = cos T î + sin 7 ĵ. Use the Theorem above to find the…

A: This is a problem related to vector calculus. Based on the general formula and concept we will…

Q: 1.The electrical voltage in a certain region is given by V(x,y,z) = 5x² -2xy + xyz. a) Find the rate…

A: Gradient of a Function:   Let f(x,y,z) be a function in ℝ3. The gradient (denoted by ∇f) is given by…

Q: 18.) Compute the directional derivative of f in the given ✓ given points P. 3 a) f(x, y, z) = xy² +…

A:

Q: C₁: r₁(s) C₂: r₂(t) C3 r3(u) = = = (s 2)i+ (2s² - 1)j + k 2t² i + (3t+7)j + (t+1) k (SER) (t = R)…

A: for the given vector functions for the curves C1,C2 and C3 To answer the given questions.

Q: Let F = –9zi+ (xe"² – 2xe³) }+ 12 . Find ſg F ·dÃ, and let S be the portion of the plane 2x + 3z = 6…

A: The vector field is F→=-9zi→+xexz-2xex2j→+12k→ The equation of the plane is 2x+3z=6⇒ gx, y=6-2x3.…

Q: Which of the following is a parametrization of the line through P = (3, 10, 8) perpendicular to the…

A: Use Parametrization to solve

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: Find the line integral of ​f(x,y,z)=x+y+z over the​ straight-line segment from ​(5,4,2) to (4,2,-2)

A: Note:- Since you asked multiple question ,according to our policy we can solve only first question…

Q: Evaluate the circulation of G = ayi+zj+ 7yk around a square of side 9, centered at the origin, lying…

A:

Q: Find the curl and also the divergence of F(x, y, z) = (x²z, e" + zz, xyz)

A: The objective is to find the curl and divergence of Fx,y,z=⟨x2z,ey+xz,xyz⟩ Curl and divergence of…