1. If 4 = xy i+yzj+zxk, find curl4 and curl curl A at points (1,2, –3).

Q: Determine L{5 – 3t + 4sin2t – 6e"} by using the Laplace table

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Q: 7. In A ABC,X is the centroid. A A. If CW = 15, find CX and XW. W B B. If BX = 8, find BY and XY. C.…

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Q: x y 11. Use Green's theorem to evaluate O In(1+ y) dx –- dy , where C is the triangle with vertices…

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Q: Define: T:P, → R by T(P) = [ p(x)dx. What is the kernel of T ?

A: Given that: T:P2→RTp=∫01px dx

Q: (B) If A = x' y z' i- 3 x'y*zj+2 x y k, find curl of A.

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Q: Find div F and curl F if F(x,y,z) = x³i - 6j+yzk.

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Q: 6. If Z is the ocentroid of AWXY, WR = 87, SY = 39, and YT 48, find each missing measure. W a) WS =…

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Q: 20. Find curl(F), where F(x, y, z) = xyz¹i+x²zªj + 4x²yz³k. a) (-4xyz³)j + (xz¹)k b) x²yj+xz¹k c)…

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Q: I need the answer as soon as possible

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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: Fined Fhe boundled by Ahe Cure area 2. x+Y= 3 %3D -33-j` and ど= %3D Ans wer

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Q: Find the EXACT Jacobian a(x,y) d(u, v) 1 1 - -— (9u - 4v), y = —— (3u +3v) 4 4 X = for the following…

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Q: Let f(x,y, z) = xy – yz and v [2y, 2z, 3x]. Find Curl(fv).

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Q: If u = x°f(x/y) according to Euler's theorem xUx + yuy is 5u %3D

A: given that u=x5fxy verify whether xux+yuy=5u is true or false

Q: F(x, y, x) = i + 3xj + 2yk And G(x, y, x) = xi - yj + zk. Find the Curl(FxG).

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Q: %3D S.

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Q: Part 3 of 6 Note that N dS = VG(x, y, z) dA, and recall that VG(x, y, z) = (curl F). NdS = (2yi + (y…

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Q: Which of the following would be a line of reflection that would map ABCD onto itself? 3 B 2 D Ox=1…

A: For the solution follow the next steps.

Q: C Find the firet order parhal derivohve of fx,y,2). e W y-10y²23+ 43x hCs, t) =° t*In ts) + 32 4,5…

A: We want to find first order partial derivative of the given functions.

Q: If F(x, y, z)= xz i  + xyz j - y 2 k find curl F

A: given: F(x,y,z)=xzi+xyzj-y2k we have to find the curl F. as we know that if we have F→=Fxi+Fyj+Fzk…

Q: If a =i+j+ 4k|and b = i+j+ 2k| Compute the cross product a x bl a xb= il+ j+ kl thin pr oblom

A: Use cross product

Q: Compute I = (2x²132²y+ 4xy)ax +(x'+2x²-y') dy+zdz along The curve C C4U Cz UG given in the figure…

A: Given To compute I=∫C2x3+3x2y+4xy.dx+x3+2x2-y2dy+zdz along the curve C=C1∪C2∪C3 given in the figure.

Q: Evaluate | CurlF nds F(x,v,z) = - yzi + xzj – xyk, and S is that part of the cylinder 4= x² + y²…

A: Given function is  Fx,y,z=yzi+xzj-xyk To evaluate ∬SCurlF·nds where S is the part of the cylinder…

Q: Evaluate O F.dT where +(3y %3D y + 1 and C is the triangle with vertices: (0,0), (6,0), (3, 5).

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Q: In AEFG, L is the centroid. If LJ=9 find EL. H J E K

A: We have given a triangle. In which LJ is the centroid. And we have to find EL

Q: 39. Show that the graph of r =t sin ti + t cos tj + t'k lies on the paraboloid z = x² + y².

A: Here we compare r as its basic equation to prove this.

Q: If F(x, y, z) = –2i – 2æj – yk and G(x, y, z) = –2xi – yj – 2zk, find curl(F × G).

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Q: Find the upper bound of e²²+1 zp- (z – 1)2 + 5“ where C is the circle |z – 1| = 2.

A: The integral ∫Cez2+1(z-1)2+5dzwhere C is|z-1|=2 To evaluate the upper bound of the integral

Q: Find the decomposition of a(t) a = arT + așN into tangential and normal components for r(1) = (5t,…

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Q: Evaluate I = Jc(sin ¤ + 2y) dx + (2x + y) dy for the nonclosed path ABCD in the figure. D А 3 (0,0),…

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Q: 45. If A = (y – 2x )1 + (3x + 2y)j, compute the circulation of A about a circle C in the xy plane…

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Q: „If A = 2xzi - yz} + 3xz'k then find curl (curl A) at (1, 1, 1). %3D .If o =x'yz and A = 2xz1- yzj +…

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Q: a) Find the curl V×Fif F = (y',2xy,yz)

A: Since you have posted more than one question, we solve the first one for you. For the remaining…

Q: 4 Let y = U2 = -7 U1 = -4 4 -6 -2 -9 Compute the distance d from y to the plane in IR° spanned by u̟…

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Q: (B) If A = x³ y z° i- 3 x³y*zj+2 x y k , find curl of A.

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Q: Find curl(zi + xj+ yk).

A: Using definition of curl of vector.

Q: If A = 3.4xyâ + (1.7x² – 6.8y)âŷ, the circulation of A around the closed path shown below is

A: In this question, we have to find the circulation of vector A along the given closed field in fig.…

Q: 5. Find the curl of U = e*yax + sin(xy) a, + cos² (xz) az. A. 2z cos(xz) sin(xz) a, + [x cos(xy) –…

A: FORMULA USED- For  f¯=pax+qay+razcurl f=axayaz∂∂x∂∂y∂∂zpqr

Q: Given F = xyi + 1(x – y) j+ 1(x + y) k, (1) Compute the fundamental cross product F, xF, =

A: Since you have asked multiple questions, we will solve the first question for you. If you want any…

Q: Suppose F(x, y) = (2 + 5y, 6z – 5y²). Use Green's Theorem to calculate the circulation of F around…

A: Given : vector field F→x, y=x2+5y, 6x-5y2 and triangle C oriented counter-clockwise with vertices…

Q: 2. If o = x²yz³ and F(x,y,z) = 3yzi + x²j + (x cos y)k, find: a) grad o %3| b) div F c) curl F

A: Given:  φ=x2yz3F→x, y, z=3yzi→+x2j→+x cos yk→ To Find:  a grad φb div F→c curl F→

Q: In AFGH, M is the centroid. If FM=20 find FK. G J K F H L

A: Given: In △FGH,  M is the centroid of the triangle. FM = 20

Q: If f=x yi- 2xz}+2yz k, find curl F at (1, 1, 1).

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Q: FIND V= (eX*z) čx + 2xy Èy+(xyi z³) &z THE CURL OF

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Q: (b) Given  = (x²y)î + (xz – z²)f – (xyz)k, determine the following at point (1, 1, 2): (i) V- Â.…

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Q: Qz: IF U=h cx,g )= Lnce+ ě).show that %3D Sy

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Q: (a) If A = x³yi + (xy + yz²)j + xy³k; B = y²zi – 3xz²j+ 2x²yk; ¢ = 3x²y + xyz – 4y²z? – 3 determine,…

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