Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi – 2xzj + yzk; (7, –9, 5)
A: Given vector field F(x,y,z) =x2 z i -2xz j +yz k ; (7 , -9 , 5)
Q: 4. If the following vector field is irrotational (i.e. zero curl), А 3 (аху + Bz3)а, + (3x? — 62)а,…
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Q: Find the divergence of the vector field F <7", 22°, zy* div F -
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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: c) Show that the vector field W(x, y, z) = (2yz+ xz – x², –2xz – yz + y?, y² – x² + z²) - - is a…
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Q: 4. Is this vector field F(x,y)=(ycos x)ĩ +(sin x+ y)j being the path-independent field? Please show.
A: To check if the given vector field is path-independent field or not. Given:
Q: Compute the curl of the following vector field. F = = (3z2 sin y, 3xz2 cos y, 6xz sin y)
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Q: Verify if div(curl F) = o for = (x - y) i+ (x +y)j+zk.
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Q: 4. Is the vector field F(r, y, :) = (yz,rz, ry) conservative? Justify your answer.
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Q: Find the directional derivative of the field f(x, y, z) = In(4 x) at P = (1, –2, –5) in the…
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Q: Find the curl of the vector field F→(x,y,z)=e^xsinyi→−e^xcosyj→+xyk→at the point (10,9,24).…
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Q: Find the divergence of the vector field F(x, y,z) = x²zi – 2xzj + yzk and the point (2, -1, 3).
A: Divergence of a vector field: The divergence of a vector field F = (P, Q, R) is given by, The given…
Q: 5. Compute div F and curl F if F = (2x – cos y)i – x²e32j + (z² – 7x)k. 6. Determine if the vector…
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Q: 2. Show that V(V × F) = 0, here vector field is twice differentiable. %3D
A: This question is from vectors.
Q: Let u = (x²yz, ry z, ryz?). Compute curl i
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Q: 3. Show that the divergence of a curl is zero.
A: according to our guidelines we can answer only one question and rest can be reposted
Q: Evaluate the line integral of the vector field (3x2 + 3y + 2xy, 3y2 + 3x + x2) along the curve y = x…
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Q: If U = 2x²yzi + yzj - z*xyk then find curl U at point (1, 2, 1).
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Q: (15) Find the divergence and curl of i = (ryz)î + (3x²y)ĵ + (æz² – y²z)& at point (2, –1,1).
A: Given v→=xyzi^+3x2yj^+xz2−y2k^ We have to find the divergence and curl of v→ at point 2,−1,1. If…
Q: The directional derivative of the field u(x, y, z) = x² – 3yz in the direction of the - vector (i +…
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Q: Is there a vector field Ğ on R³ such that curl Ġ = (xyz,–y*z³,y*z*)?
A: the given function is, G→=xyzi^-y4z3j^+y3z4k^ If there exists a vector field G then the divergence…
Q: Compute the line integral of the vector field F = (3zy1, 4z, -y) over the path c(t) = (e*, e', t)…
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Q: Find the gradient vector field (F(x, y, z)) of f(x, y, z) = In(4x + y + 62) . F(1, y, 2) =
A: we have to find the gradient vector field of f
Q: A scalar field is given by f = x2/3 + y2/3, where x and y are the Cartesian coordinates. The…
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Q: If F = Pi+Qj+ Rk, prove that div (curl F) = 0
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Q: Find the curl of the vector field F(x,y,z) = x²zi – 2xzj + yzk and the point (2, -1, 3).
A: Let the given vector field is :
Q: compute dr for the vector field where Cis the line segment from Co.o) to Cli3)
A: Given vector field is, F=1+x2,xy2 The objective is to compute ∫CF·dr, where C is the line segment…
Q: If F = xyz i+ zxj +xy'z k then find curl F at (1, 2, – 1).
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Q: Sketch the vector field on given byF(x, y, z )= z K
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Q: (3)If F = (x points (2,1,1) ² yz, xyz² , zy² ). Find curl curl F at
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Q: (2) Find the line integral of the vector field F(x, y) = (-1,3) along the path from (2, 3) to (2,…
A: The vector field F→=-1, 3To find line integral of vector field along the path 2, 3 to 2, 5
Q: Find the curl of the vector field F=(2xyz, -xy,-z^2)
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Q: What is the largest possible magnitude of Curl(F) where F(x, y, z) = (4, a/9 – y?, 6z)? у, х
A: Given that F→x,y,z=4,x9-y2,6z
Q: The vector field F is shown in the xy-plane and looks the same in all other horizontal planes. (In…
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Q: Find the curl of the vectòr field F(x, y, z) = 2xyzi + 8yzj + 5zk
A: According to our guidelines we are supposed to do only one question. Kindly repost other question…
Q: 3) Evaluate curl(F F(x, y. =) = (y=+2xy, 2xy + x + =, xy + 23z) to show that is conservative.
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Q: i) Show that F is a conservative vector field.
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Q: Show that the vector field F = 2xyi +(x² - 2y)j is conservative and evaluate the line integral (F•dš…
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Q: Consider the curve C from (-2, 0, 1) to (6, 5, 2) and the conservative vector field F(x, y, z) =…
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Q: Show that there is no vector field G = (P,Q, R) where P, Q and R have continuous second order…
A: Recall a result, If G= (P,Q,R) is a vector field on IR3 and P, Q and R have continous second order…
Q: Let i = (x²yz, ry z, zyz?). Compute curl i
A: The given vector is: u→=x2yz, xy2z, xyz2
Q: 6. Show that F = [y? cos x + z3, 2y sin x – 4, 3xz2 + 2] is a conservative force field. Find the…
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Q: Find a vector potential field for Ġ = [6xz+x³, –3r²y – y², 4.x + 2zy – 32²], i.e. find F such that V…
A: The solution is below.
Q: Show that Green's Theorem holds for the vector field F(x, y)=(x +y, 3x) at a square of side 2.
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Q: 3. Show that the vector field F = -C with C> 0, is conservative and find its potential.
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Q: Compute the divergence and curl of F= -(z³-3x)j+4y²k+x²yi
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Q: Let F(x, y, z) =⟨3x2y+az, x3,3x+ 3z2⟩ be a vector field. For what values of a is F conservative?
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Q: Calculate of A= Xzi- 2x*yzj+2yz'K at ( 1,-1,2). the Curl and Divergence
A: Given A = xz3i-2x2yzj+2yz4k Compare it with A = Axi+Ayj+Azk Hence Ax = xz3Ay = -2x2yzAz = 2yz4 Then…
Q: Find the curl of the vector field at the given point. F(x, y, z) = x²zi - 2xzj+yzk; (9,-9, 9) curl F…
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- Find curl F if F(x,y,z) = 16y°z5 i - 8x³z8j - 7xy4 k. curl F = (-28xy3 + 64x³z7) i + (7y4 + 80y°z4) j + (-24x²z8 - 80y4z5) k 3,7 O curl F = (-28xy + 64x°z7)i + (7y4 + 80y5z4) j + (24ײz8 + 80y4z5) k O curl F= (-28xy3 + 64x³z7) i+ (7yª + 80y5,4) j + (24x²z8 - 80y4z5) k = = (28xy³ + 64x³z7) i+ (7y^ + 80y5z4) j + (-24x²z8 - 80y4z5) k4) Find the adjoint of the operator Lu = u" + 4u' – 3u, where u'(0) = -4u(0), u'(1) = -4u(1).Find div F and curl F if F(x, y, z) = xºi-2j+yzk. div F= curl F=
- (5,4), A' 3 (5, 9), В' — (11,—3), and C" 660. Let A 3D (1,5), В — (3,1), С %3 (5, 4), А' %3 (5, 9), В' 3D (11,—3), and C' %3D (17,6). Show that there is a dilation that transforms triangle ABC onto triangle A'B'C'. In other words, find the dilation center and the magnification factor.VI. = (xy, y,z?+y) , f(x,y,z) = xy. Find Curl(F) 2. Div curl(F) 3,. Div (fF) 4. Divgrad(f)z is a complex variable z=x+iyShow that f(z)=((z^2)+1)/((z^2)-3z+2) is continuous for all z outside |z|=2
- If f(x) = x2 + 2xy + y² + xyz + z² Find V. Vf or div[grad(f)I Find VXVf or curl[grad(f)]Evaluate the line integral 3xy ds where C is the Segment Joining (-5,7) to (3,1) line SegmentEnter a rule for a transformation that maps ASTU to AS 'T 'U'. LU2 S (4, 3) → S' T (4,-3) » T' U (-4,-3) U' So, the transformation divides each (select) unchanged. by but leaves the (select) The rule is (x, y) →
- 13- a) b) O лу z=f(x,y) = cos(2-2x + 2) + x²-x² COS Which one of the following is the gradient vector of f(x, y) at the point P = (0, 1)? (2-1) i + 1/2 j (-7/2+1) - 7/1 (2-1)1-5/1 (-7/2-1) 1 + 7/1 • (-/-1) i-7/1(b)Find the derivative of g in the direction of ā = 2i+ curl w at point (0,-1,1): where 8 = In- u + 2 = z(xy+z? } , w = cos -i+ xe*lj+ xyz k U = z W = COS- yz