Problem. Use Green's Theorem, So ӘР dA, ду Рах + Qdy дх to evaluate the line integral, (–x² + e" In y)dx + (x+ y² + et dy, where C is the triangle with the vertices (1, 1), (2, 1), and (2, 2), and the positive (counter- clockwise) orientation.

Q: Evaluate L₂Lova (4-3²) dydx -√4-x² by using polar coordinates.

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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: Find polar coordinates (r,θ) where r < 0 and 0≤θ≤2π of(√3,−1)

A: Given point in the rectangular coordinates is 3,-1. To find the polar coordinates r,θ, where r&lt;0…

Q: Calculate the integration of (A" - dlP2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector…

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Q: Consider the following function. T: R2 - R3, T(x, y) = (2x², 3xy, y²) Find the following images for…

A: Let us consider the given transformation T:V→W then the transformation is said to be linear…

Q: (b) part of parabola y = −2x² from (−1, −2) to (2, —–8)

A: Given Equation of parabola y=-2x2 from -1, -2 to 2, -8.

Q: The scalar component of H parallel to the line y=1, z=2 where H = -2a, + 3as- 4a, at p (1,90, 2) -3…

A: Given: H=-2aρ+3aϕ-4az p=1,90,2

Q: Find an expression for a unit vector normal, no, to the surface x = (4 – cos (v)) cos (u), y = (4 –…

A: The complete solutions are given below

Q: hat is the scalar equation of the xy plane?

A: Given query is to find the scalar equation of the XY plane.

Q: Consider the three following points of R'. A = (0, 2, 2) B = (1, 1, 1) C = (-1, 1,2) (a) Find the…

A: The scalar equation of a plane is of the form: ax+by+cz+d=0, where a, b, c ,d are constants. The…

Q: 3. Find a set of symmetric and parametric equations of the line passing through the point (1, 4…

A: This is the problem from the vector algebra and 3D geometry.

Q: Let F = (3z + 3x²) i + (6y + 4z + 4 sin(y²)) 3+ (3x+4y+6e²²) k (a) Find curl F. curl F = (b) What…

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Q: Is sin(z) bounded in the complex plane?

A: In mathematics, a function is said to be bounded if there exists a real number M such that the…

Q: 6. Find parametric equations for the line of intersection of the planes 2x – y + z = 4 and 3x + y +…

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Q: 285. Find the scalar equation of the plane that passes through point P(-1, 2, 1) and is…

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Q: Represent the line segment from P to Q by a vector-valued function. (P corresponds to t = 0. Q…

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Q: Prove that a parametric function given by I= 21 + 312 y = t² + 21 satisfies the equation dy + 2 dr…

A: see the details solution in below