Find the line integral F.dr of the vector field F=ax k over a curve C defined by a C rectangle in the xy plane of length L along x and Walong y. Start at the origin and proceed along the x axis. Set up the integral even if you know the answer in advance.

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Q: A vector field F and contour lines of a potential function for F are shown in the figure. Calculate…

A: From the diagram given in the question, ∫F dS=∫C∆v.dS=v(Q)-v(P)=4-1=3

Q: 9) Check whether the vector field F = (-cos x cos y, sin x sin y, - sec² z) is a gradient vector…

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Q: Suppose the field lines of a gradient field F: R2 + R² are hyperbolas and the length of each vector…

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Q: Determine whether the line integral of each vector field (in blue) along the oriented path (in red)…

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Q: Determine whether the line integral of each vector field (in blue) along the oriented path (in red)…

A: For a path perpendicular to the vector field, the line integral is zero.For the path is along the…

Q: Determine the curl and divergence of F(XYZ) = xye* ^-x³yze²^ + + xy²e¹ k

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Q: Compute the line integral of the vector field F = (3y, −3x) over the circle x² + y² = 81 oriented…

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Q: Find the line integral of the field F = over the portion of the ellipse * + y = 1 lying in the first…

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Q: y² cos(xy?) – ay sin(æ²y) Let it be 7 : R² → R², (2ary cos (ay?) – ža² sin(a²y)/ a vector field.…

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Q: Let C be the curve with parametrization r(t) : ,0 . Find the value of F · dr.

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Q: Sketch the slope field for the points (ti, y;) where at and dy dt y-2 Z₁ = -1 + 0.25(1-1) = for…

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Q: The plot of the vector field F is given below. Place the following line integrals in the correct…

A: For the given vector field F , to place the line integral in correct order :-

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: 6. a. Sketch a vector field F and a closed curve c with (make it obvious): SF dF >0. b. What can you…

A: Let us consider a vector field F and C be the closed curve shown below. Since all arrows are in the…

Q: Specify the component function of of vector field F in R2 where the flow of F is around the origin,…

A: To Specify : The component of a vector field F in R2 where the following conditions are satisfied:…

Q: Find the line integral F.dr of the vector field F=ax] over a curve C defined by a C rectangle in the…

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Q: 3. Find the line integral fF.dr where C' is the circle of radius 5 in the xz-plane oriented…

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Q: Suppose f = sin(x - 2y), and the vector field F = ∇f. Find the following curves: C1, which is not…

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Q: Consider the vector field F = ⟨ 1 , y ⟩ .Compute the path integral of this field along the path:…

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Q: Consider a Vector field F-(e²cosy + yz, xz - ex siny, xy + 2). determine if the field is…

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Q: 12. Evaluate the curl of the following vector field at the point (0,1,2): F = (x + y + z, x? + y? +…

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Q: 5. Find the gradient vector field of f = √2x² + 2y² and sketch it.

A: Given: Let us consider the given vector field, f=2x2+2y2 To find: The gradient vector field f and…