Consider the field F(x.y.z) = 1 (x +y) i+1 (x5+y)j+1 (x2 +y2) k. (a) Integrate F.ds around the rectangle defined by the points (0.0,2,0). (3.9,2,0). (3.9,3.7,0), and (0.0,3.7,0). (b) Integrate F.ds around a circle on the x-y plane of radius 6, with the center at the origin.

Q: find the curl of U = exy ax +sin(xy)ay + cos2(xz) az

A: U=exyax+sinxyay+cos2xzaz

Q: (c) If and are smooth scalar fields, show that V x (6V) = Vox V

A:

Q: 20) For each vector field F, evaluate the circulation along the curve C consisting of the portion of…

A: Step 1:Step 2:Step 3:Step 4:

Q: Suppose f(x, y) = x² + 2æy+ y². Which field plot is Vf? Justify your answer. 鹿

A:

Q: Determine the curl and divergence of F(XYZ) = xye* ^-x³yze²^ + + xy²e¹ k

A: To find- Determine the curl and divergence of Fx, y, z = xyex i^ - x3yzez j^ + xy2ey k^.

Q: Match each of the functions (a)-(c) with the corresponding gradient vector field from those in…

A: We have to match the gradient vector field

Q: - Find div F and curl F if F(x, y, z) = 10y¹z7i – 17xªzºj – 3xyễk. div F= curl F=

A: The general form of a vector-valued function in three dimensions is given by F=F1i+F2j+F3k, where…

Q: Graph

A:

Q: Find the divergence of the field F. F = - 4x5i + 2y5j-8z5k OA. - 4x4 +2y4 -8z4 OB. 20x4 +10y4 - 40z4…

A: To find the divergence of the field F.F=-4x5i+2y5j-8z5k

Q: Given the 2-D vector field : G(x, y) = (2y)î + (x)j and the triangular curve T : line segments from…

A: Given: G→x,y=2yi^+xj^ Triangular curve T, line segments from point A0,0 to point B4,0 to point D4,2…

Q: 2. Let F = 3.xyz i – 4xyz j + 2xyz k . Find div F and curl F. -

A:

Q: =x-y+3|

A: I have provided a graph of this in step2

Q: dt Use parseval's identity to prove that J a? +6²+?) 2ab (a + b) TC

A:

Q: Let F (8xy, 3y, 8z). = The curl of F = (000). Is there a function f such that F = V f? ☐ (y/ (y/n)

A: Step 1: Step 2: Step 3: Step 4:

Q: Find the work done by the Öeld F = yzi + (xz + 3)j + xyk along the line joining the point A(1, 2, 0)…

A: Given field is,  F = yz i^ + xz+3 j^ + xy k^   The given points is A(1, 2, 0) and B(2, 0, 3). So,…

Q: Explain how to compute the Jacobian of the transformationT: x = g(u, v), y = h(u, v).

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: Let F = (3z + 3x²) i + (6y + 4z + 4 sin(y²)) 3+ (3x+4y+6e²²) k (a) Find curl F. curl F = (b) What…

A:

Q: Compute w(v), where w =(x-y)dx+(x+y)dy is a covector field and v = (x/y)d/dx-(y/x)d/dy is a vector…

A: Given: w =(x-y)dx+(x+y)dy  v = (x/y)d/dx-(y/x)d/dy

Q: Is = xjx + yjy+zźz3 an inner product on R'?

A: No it is not an inner product.  Inner product looks like a dot product.

Q: If F = xyz i+ zxj +xy'z k then find curl F at (1, 2, – 1).

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: Ex: Find the work done by the vector field F = (y-x²)i + (z - y²)j + (x-z²2)k Over the curve r(t) =…

A: Given: F=y-x2i+z-y2j+x-z2krt=ti+t2j+t3k

Q: 6. A mountaineer is She begins her jo (a) Calculate th

A: Directional derivative at point is obtained by derivation of the function at x and y variables or…

Q: 2x 2y Consider the vector field F = |x² + y2’ x² + y² (a) If C1 is the unit circle x² + y² = 1,…

A: Compute the circulation and flux using parameterization:  ∮C1Fdr=∮C12xx2+y2,2yx2+y2·dx,dy…

Q: Compute the curl of F = (3y2, ay, 22).

A:

Q: Plot the gradient vector field of f together with its contour map. (a) f(x,y)=4- -4-4-4 (b) f(x, y)…

A: Given:  a fx, y=4-x24-y24b fx, y=x2+y2 To Plot the gradient vector field and contour map.