a) If A=xz' i-2x²yz j+2yz k, find VxA (curl A) at the point (1,-1,1).

Q: Find div F and curl F if F(x, y, z) = x²i – 5j + yzk. div F= curl F=

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

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Q: The curl of- yi+z+xR"

A: In this question, we find the curl of the vector function by using the determinant method.

Q: Let R = {(x,y): |x| + |y| ≤ 2}. Use the transformation x=u+v, y=u-v to evaluate ∫∫ ((x^2)*(e^y))dA

A: Consider the given: R=x,y:x+y≤2x=u+vy=u−vA=111−1=−1−1=−2=2

Q: Calculate grad div F+ curl F at P(-1, 1, 1) where − = (3xz²)i + (xy)j + (2yz)k. O 7i+ 4j - 3k D-3i -…

A: we will find the required.

Q: of ū at the poir 01

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Q: e'ス+×cos(2) 3. (o'1'e)と Flsye)-xをえゃxそsQe)s Find Curl at

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Q: Find the curl, the divergence and the potential (if it exists) of F = (2x + y², 2ry + 3y²z*, 4y°z³)

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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: 18)Find curl F and div F if F(x,y,z) = exsiny i + esinz j + e²sinx k

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Q: y = x^2 -5x+4  y = x − 1 Axis of rotation: x = 7 how would i use the disk method in this not…

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Q: Current Attempt in Progress Find curl(6z i + 7x j + 9y k). curl(6z i + 7x j+ 9y k) = ( i Di +( i )j…

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Q: se the given transformation to evaluate the integral. J 6z + 3ydA, where Ris the parallelogram with…

A: we have given: x=13u+v and y=132u-v  u=x+y, v=2x-y Now, Consider the integrals, ∬R6x+3ydA where, R…

Q: Find div F and curl F if F(x, y, z) = 4y°z'i – 11x"2°j – 4xy°k. div F= curl F=

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

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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: 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: find curl (grad Q).

A:

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).

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Q: (b) tan(x/y) = z+y

A: We will solve the problem

Q: (5. 2y+z2)i+ (zy? 2)j+ (2 - 3. zy)k, find curl a at the point (4,3,3). (zy²2)j+ (c) Given that a = I…

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Q: Use Green's Theorem to evaluate(¹-28) O-96 O-75 O 105 -2y) de- (62-4ry") dy where C' is shown below

A: We want to calculate the integral ∫Cy4-2ydx-6x-4xy3dy

Q: Find curl(F x G) = V x (F x G). F(x, y, z) = i + 9xj + 7yk G(x, y, z) = xi - yj + zk

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Q: 2 Locate the numbers z₁+z₂ and z, - z₂ vectorially when z₁ = 2i, z₂ ==-i. 3

A: Use addition the evaluate these numbers then plot it

Q: Let the following be: 7 = ri+yj+zk. Given this, please demonstrate the fact that the div (r) = 3. As…

A: Here the given vector is                                     r→=xi^+yj^+zk^ Now we find the div(r→)…