Consider the conservative vector field Ġ(x, y, z) 2x sinh (x – y) + 2axy, sinh (22 – y) − 3Vy − z2 +a, 6 Vy - 2 - Let C be the line segment from (-1, 1, 1) to (2, 4, 0). Compute for the real number a if [G. dR= = = −1.

Q: (x, y) (1.0) (2, 2) (3,0) (0, 1) (-2,2) (0, 3) F(x, y) (0, 1) (-2,2) (0.3) (-1,0) (-2,-2) (-3,0)…

A: This is a question of vector calculus.

Q: OSketch the vector field F(x, y) = -5i – 5j and calculate the line integral of F along the line…

A: Solution:-     Given that, F→ x,y=-5i∧-5j∧we have to calculate the line integral ∴we have to…

Q: Calculate the divergence of the vector field F (x, y, z) = − 10 sin(2xy)i — cos(x³y)j. (Give an…

A:

Q: Find the gradient fields ƒ(x, y, z) = (x raise to the power 2 + y raise to the power 2 + z raise to…

A: Given:            f(x,y,z)=(x2+y2+z2)−12

Q: Let C₁ be the directed line segment that starts at (2,0) and ends at (-3,-5) and C₂ be the parabola…

A:

Q: 1. Find the line integral in a vector field a curve consisting of 2 parts. First, the straight line…

A: Given F→=y,x+2y We have to find the ∫CF→⋅dr along the given path.

Q: Find the curl of the vector field F. F = (x-y+z)i+ (6x-y+7z)j+ (9x +6y + z)k curl F = i+

A: We have to find the curl F

Q: Consider the vector field v(x) = 2+y22-2²y2j+2k. Calculate y dr, where C is the straight line from…

A:

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: 7. Sketch the vector field F = (x − y)î + yĵ. Identify where F₁ vanishes. Identify where F2…

A: According to our guidelines,i can solve only first please reroute the remaining question.

Q: 1. Consider the vector field F(r, y, 2) = (* - ", e – a*, z – sin(ay2). (a) Sketch the vector field…

A:

Q: Evaluate the 1-form φ = x2yz dx − z dy on the vector field V (x, y, z) = xU1(x, y, z) − yzU2(x, y,…

A: We need to evaluate the 1-form of  ϕ=x2yz dx - z dy.....(1) in the vector field  V(x,y,z) = x…

Q: Let C₁ be the line segment from the point (-4, 8) to the point (2, -4), C₂ be the arc on the…

A:

Q: 1. For each of the following vector fields F(1, y), decide if there is function f(z, y) such that F…

A:

Q: Show that the vector field F(x, y, z) = (-4y cos(4x), 4x sin(–4y), 0) is not a gradient vector field…

A:

Q: Question 6. Consider the relation R(ABCDE) and its functional dependencies set {AB->C, C->E, B-> D,…

A:

Q: 1. Determine whether F(x, y) et sin yi + e" cos syj is a conservative vector field.

A:

Q: 3. Let f: R2 → R be the function which satisfies for all (x, y) E R² that f(x, y) = 100 – x² – 2y?…

A: A scalar function f(x,y) is a rule that is used to associate a number, or quantity with a particular…

Q: Find the curl of the vector field F = (3y cos(x), 5x sin(y))

A:

Q: Show that the vector field F(x, y, z) = (-ycos(8x), 8x sin(-y), 0) is not a gradient vector field by…

A:

Q: 3.For the vector field F = 2(x + y) - 9 2x² + 2xy, › evaluate fF.ds where S is the upper hemisphere…

A:

Q: Consider the function f(x, y) = exy. (a) (b) (c) Determine the vector field F = Vf. Evaluate F. dr…

A: (a) ∇f=fxi+fyj (b) A gradient field is always irrotational so its integral will be path independent.…

Q: (9) Determine whether or not the vector field is conservative. If it is conservative, find a…

A: F=Pi+Qj is conservative if ∂Q∂x=∂P∂yGiven F=cos x+ sin y+y sec2xy-2x+y2-2xy2i+2y+2xy-2x2y+xsec2xy+x…

Q: Sketch the given vector fields by drawing some representative vectors. (a) F(x, y) = (x − y) î+xî…

A: Given:  a F→x, y=x-yi^ +xj^b F→x, y=y, -xx2+y2c F→x, y=2yj To sketch the given vector field.

Q: Suppose F = (2y, -2x). Complete the following table of values of F. Values of F y = 1 y=0 y = -1 x =…

A: