Use Green's theorem for the work done by the force F= (x - y)i + (x + y)j, for the shaded region R of the image YA x² + y²=4 R x² + y² = 1 +

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: Parameterize the intersection of z = - Vx² + 7y² _and x² + y? + z? = 200

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Q: Your friends correctly calculate the gradient vector for f(x, y)=x²+y at the point (2,-3) as…

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Q: Q3. Find out values of a, b, c for which curl of vector V is zero, where V = (2xy+ 3 yz) i +(x² +…

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Q: he vector v = , is tangent to the surface x2 + 2y3 - 3z2 = 3 at the point (2, 1, 1).  Find a.

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Q: c) Verify Stokes's Theorem for F = (x²+y²)i-2xyj takes around the rectangle bounded by the lines x…

A: Stoke's law is given as ∫cF→.dr→=∫s∫∇×F.n→ds F=x2+y2i^-2xyj^ dr→=(dxi^+dyj^) So F.dr=x2+y2dx-2xydy…

Q: 4. Consider the vector function r(z, y) = (x, y, x² + 2y*). (a) Re-write this vector function as…

A: For the given vector function, PART A The surface function is given by, f(x,y)=xi^+yj^+(x2+2y2)k^…

Q: Find the work done by F over the curve in the direction of increasing t. F = 4zi + 4xj + 4yk, r(t) =…

A: Note that : Since you have posted multiple questions, we will provide the solution only to the first…

Q: Let F = Jo Use Stokes' Theorem to evaluate F. dr, where C is the triangle with vertices (10,0,0),…

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Q: 3. Let F and G be vector fields with differentiable components. Express curl (F x G) in term of div…

A: Introduction: The curl of a vector is a vector-valued function. It is the cross-product of the…

Q: Consider the following function. T: R? - R, T(x, y) = (2x?, 3xy, y²) Find the following images for…

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Q: Sex. (x+y)ds where C is the straight-line segment x = 3t, y = (3-3t), z = 0 from C (0,3,0) to…

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Q: Find an equation of the plane tangent to the Bohemian dome S described by the vector function R(u,…

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Q: Vector F is mathematically defined as F = M x N, where M = p 2p² cos + 2p2 sind while N is a vector…

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Q: Find the work done by the force F = 2i - 7j in moving an object from the point (2, 1) to the point…

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