(10) Given that the vector field F= 2z i- 3 x j + 4 y k Evaluate f F. dr where S is the portion of the paraboloid z = 16 - x² - y? for z 2 0 in the first octant

Q: 4.) Verify the Expansion of the triple vector product A x (B x ) = B⋅ (A·C) - C (A. B) by direct…

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Q: Let A be an m x n matrix, and let B and C have sizes for which the indicated sums and products are…

A: If the product AB is defined, the entry in row i and column j of AB is the sum of the products of…

Q: Sketch the vector field in the plane along with its horizontal and vertical components at a…

A: We shall use MATLAB to plot the given vector field on the circle.  MATLAB CODE F = @(x,y)…

Q: F = (x² +y², y² +z?,.

A: on solving this we get the

Q: 2. For the vector field V = (7x³ + 2y2²)i + (4x²z - 7y²+3)j + (4y³ +2² -32²) k find the divergence…

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Q: Compute feF. dr where C is the curve of intersection of the paraboloid z=9-x² - y² and the plane z =…

A: To compute the line integral ∫CF⋅dr. We have F=2x2+3zi+4ey+8xj+6z2+7yk and  C is the curve of…

Q: The surface H is defined by (x² + y²)² + z = 1; z ≥ 0. The vector field A(r) is given by A = (x, y,…

A: The surface H  is defined by    .The vector field  is given by   .We have to sketch the surface H.

Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Given that v=<x-y, z+y+9, z2> and the given curve is y=1-x2-z2,y≥0 To find: The value of ∬S…

Q: 2. Find the curl of the vector field. F = z°e* sin(2 y)i – e' cos yj+ xyzk to

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Q: Let A be the vector potential and B the magnetic field of the infinite solenoid of radius R. Then

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Q: sketch the the vector field F(1.4)= i + 1/ 45 2

A: First component is  = 1 Second component is = y/2

Q: How much work is required to move an object in the vector field F= 5 y2i + 2xy J  Along the curve ,…

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Q: A net is dipped in a river. Determine the flow rate of water across the net if the velocity vector…

A: Adding the plane surface y=0 to close the surface and apply the gauss divergence theorem.

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: y X Consider the vector field u(x) = x²+²x² + y²j+6k. i Calculate y dr, where C is the straight line…

A: Introduction:  A line integral is an integral where the function to be integrated is evaluated along…

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: The directional derivative of the field u(x, y, z) = x² – 3yz in the direction of the - vector (i +…

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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: a) Find the curl and the divergence of the vector field: F = (3x + 2z?)i + (*)j- (2- 7x)R.

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Q: Consider the vector field F(x, Y, z) = 3x?yi+ (x³ + 1) j+9z²k. Let C be the circle cut from the…

A: Given vector field is  F(x,y,z)=3x2yi+(x3+1)j+9z2k C be circle cut from sphere x2+y2+z2=8 by the…

Q: If the temperature at which a certain compound melts is a random variable with mean value 115°C and…

A: We have to solve given Questions.

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

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Q: Let F be the vector field (-2 sin(2x - y), sin(2x - y)). Find two non-closed curves C₁ and C₂ such…

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Q: = + 1³ 2³ +²²³ +22+ Calculate the flux of the given vector field F where S is the sphere centered at…

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Q: 6 Find the constants a and b so that F = (ax'y°z°, x°y²z°, bx°y° z²) is conservative. You may use…

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Q: 2. A vector field is specified as G = 24xy ā, + 12(x² + 2)ā, + 18z²ā,. Given two points, P(1, 2, -1)…

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Q: Consider the vector field u(x) = Calculate (0, 4, 8). y x²+y². х 5i - x² + y²j+6k. y dr, where C is…

A: vx=yx2+y2i-xx2+y2j+6k

Q: For the vector field F = yr³i - y²j, the work on the curve y = √x from (1, 1) to (0,0) is A. B. C.…

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Q: Determine the vector field of F. F(x, y) = 12i - 4j

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Q: re f an -2, 3)

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Q: Let a vector field F(x,y)=sinx 1 + xy j be given. What is the integral representing the work done by…

A: Acoording to expert guidelines, I am allowed to answer first question only. Kindly repost the rest…