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: 6. Find the symmetric equation of the line parallel to ở = (1,4, 6) + t(−2, 4, 7) that intersects…

A: Given problem:- 6. Find the symmetric equation of the line parallel to r = (1,4,6) + t(−2, 4, 7)…

Q: Let C be the positively oriented square with vertices (0, 0), (2, 0), (2, 2), (0, 2). Use Green's…

A: Introduction: According to Green's Theorem, a line integral of a vector over a closed curve C…

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: The vector parametric equation for the line through the points (-3, 5, −4) and (5, −5, 0) is L(t) =

A: The given points are -3, 5, -4 and 5, -5, 0. We have to find a parametric equation.

Q: W= Sp { (2,0,-1,2), (d,d, 2,3) } cR find a basis for the oahogonal complement of the Ssubspace w

A: Given below the detailed solution

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: (b). Use Green's Theorem to evaluate SF. dr. F(x, y) = (e³x², 2xy), where C is the triangle from…

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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: 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: Let C be the positively oriented square with vertices (0, 0), (2,0), (2, 2), (0, 2). Use Green's…

A: Let the given square be OABC which is positively oriented.

Q: Consider two functions u(xyz) and v(xyz), where r, y, and z are independent variables. What is Vu x…

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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 C be the positively oriented square with vertices (0, 0), (3, 0), (3, 3), (0, 3). Use Theorem to…

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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: Please answer the 9th root of 615 with an Explanation.

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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: The line in R³ through the point Po(xo, Yo, zo) and parallel to the vector v = parametric equations…

A: Given that the position vector of the point is P0 (x0, y0, z0) and parallel to the vector v = (v1,…