Find the potential function for the vector (a+1,b+1,b–1) 2.3_3 2.xy'z* dx + 3x*y°z* dy +4x²y°z° dz (0,0,0) Choose a and b as the last two numeric digits of your student ID.

Q: Find the work done by the force field F(x, y, =)=(: - =', y + 3:, = + x*) in moving a particle alon,…

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Q: Find the work done by a force F = 6ỉ + 5j– 3k when a particle moves from point P(-3, 4, 5) to point…

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Q: Confirm that the force field F(, y) = 2xy°i+ 3x²y² j is conservative in some open connected region…

A: Solution:- The given function is  F(x,y)=2xy3i+3x2y2jpoint P(-9,8) and Q(6,7)we have to find the…

Q: Find the gradient vector field for the scalar function f(x,y)=sin(2x)cos(6y).   Enter the exact…

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Q: a. Show that the line integral Sc (yz — 2z) dx + (xz + 3) dy + (xy – 2x) dz is independent of the…

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Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y, z) =…

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Q: Confirm that the force field F(x, y) = 2xy³i + 3x²y²j is conservative in some open connected region…

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Q: Find the total work done in moving particle in a free field given by F = 3xyi – 5zj + 10xk along the…

A: The total work done by a vector field, F→ moving a particle along the curve r→(t) is calculated…

Q: Compute the curl of the following vector field. F = = (3z2 sin y, 3xz2 cos y, 6xz sin y)

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Q: Compute the scalar line integral x – yz ds where C is the line seg- ment from (0, 1, 1) to (1,0, 1).

A: Given  ∫C x-yz   ds    where C is line segment from (0,1,1) to ( 1,0,1)

Q: Find the flux through through the boundary of the rectangle 0 < x < 6, 0 < y < 5 for fluid flowing…

A: Given F→=x5+y  , y cos3x flux=∫cF→.n^  ds =∫∫Ddiv F dA

Q: e modulus valu

A: In the given question, the concept of derivatives is applied. Derivative We can use a derivative to…

Q: 4z² + 5dz 금(122+5) xo 4a? + 5 Part 2 of 2 ewrite the integrand in terms of u so that the integral…

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Q: A particle moves along line segments from the origin to the points (1,0,0), (1, 2, 1), (0, 2, 1) and…

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Q: A particle moves along line segments from the origin to the points (1, 0, 0), (1, 5, 1), (0, 5, 1),…

A: Obtain the equation of the plane passing through the 4 points (1,0,0), (1,5,1), (0,5,1) and the…

Q: Find the work done by the force field F in moving an object from P(-3, 7) to Q(7,5). 2x Y F(x, y) =

A: To find the work done by the force field F in moving an object from P-3, 7 to Q7, 5. Fx,…

Q: Given the vector field v=⟨0,2xz+3y^2,4yz^2 ⟩. Find the line integral of the path from (0,0) to…

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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: Compute the flux of the vector field (x, - xy*), out of the rectangle with vertices (0,0), (5,0),…

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Q: 4. Find the flow of the velocity field F = V(xy²z³) along the line segment from (1,1,1) to (2,1,…

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Q: 2. Consider a conservative force of F = (3x² - 6yz) i + (2y + 3xz) j + (1 - 4xyz') k acts on a…

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Q: Show that the force F = (y^²2² - 6xz² ) ₁² + ²xyz²³ j^² + (3 xy² z ²-6x²²Z) k IS Conservative, hence…

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Q: Find the work done by the force F 6xy i + line segments from (-4, 4) to (0, 0) and from (0, 0) to…

A: Consider  F(x,y)=M(x,y)i+N(x,y)j is vector valued function then : if ∂M∂y=∂N∂x then F is called to…

Q: Find the work done by the force field F(x, y, z) = on particle that moves along the line segment…

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Q: Show the values of the integral does not depend on the path taken from A to B (The vector field is…

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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: A particle starts at the point (-2, 0), moves along the x-axis to (2, 0), and then along the…

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Q: Find the flux through through the boundary of the rectangle 0 < x < 6,0 < y < 5 for fluid flowing…

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Q: Find the gradient field associated with the function φ(x, y, z) = xyz.

A: To find the gradient field associated with the function  φ(x, y, z) = xyz.

Q: Find work done by a force field F= in moving object along the line segment from the point (2,1,3) to…

A: Given, F=1y-x,xyz,ex2+y2+z2

Q: The work done by a force field in a moving particle around a closed path is zero.

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Q: Find the work F dr done by the force field F = (y, x, z) on a particle that moves along C the line…

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Q: Compute the flux of the vector field F = xi + yj + zk through the surface S, which is a closed…

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Q: 6. What is the corresponding vector fieldV for the scalar potential p(x, y)= In(x+ ¥)?

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Q: Find the work done in moving a particle in a force field F = 3xyi - 5xyzj + 10xk along: straight…

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Q: Find potential 9, for the conservati ve field the vector F (x, y,a)- (2xe? - y*sinx) î * sinx) î +…

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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: Show that the vector field =(-2 x²y xy²¹ is conservative by finding all its potential functions.…

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Q: a. Show that the line integral Sc (yz - 2z) dx + (xz+3) dy + (xy - 2x) dz is independent of the…

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Q: Calculate the line integral of the vector field F = -2i+ 4jalong the line from the point (3,0) to…

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Q: Find the flux of the vector field F = across the part of the plane | z = 2 + x + 3y above the…

A: Given: F¯=y,-z,x z=2+x+3y The formula to determine the flux is: ∫S∫F·nds=∫D∫(-agx-bgy+c)dA Here…

Q: Find the conservative vector field for the potential function by finding its gradient. g(r, y, :) +

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Q: Find the conservative vector field for the potential function by finding its gradient. f(x, y,…

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Q: Find the conservative vector field for the potential function by finding its gradient. h(x, y, z) =…

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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: 6. Show that the system with vector field -x + sin(y) F(x, y) : -y+ cos(x), admits no periodic…

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Q: A particle moves along line segments from the origin to the points (3, 0, 0), (3, 3, 1), (0, 3, 1),…

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Q: 3.7 If the integral| F dl is regarded as the work done in moving a particle from A to B, 'A find the…

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Q: Express the vector field D = ( x2 + y2 )-1 ( xax + yay ) in cylindrical components and cylindrical…

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Estimation

A new framework of data analysis where the new statistical methods are used for interpreting the results and analyzing the data is known as estimation in statistics.