Use Stokes's Theorem to evaluate e curlF. ds. (1) F(x, y, z) = x²y³zi+sin(ryz)j + xyz k, S is the part of the cone y² = 2² +2² that lies between the planes y = 0 and y = 3, oriented in the direction of the positive y-axis.

Q: Use Stokes' Theorem to evaluate of intersection of the plane .x+3y + 5 = 24 with the coordinate…

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Q: c) Use Stokes' theorem to evaluate F. dr where F = z' i+yJ + xk and C is the triangle with vertices…

A: Stokes theorem is used to find the line integral of the vector point function

Q: F · dr  where F  =  (x + 5z) i  +  (7x + y) j  +  (2y − z) k   and C is the curve of intersection of…

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Q: Use Stokes's Theorem to evaluate f.7 X F.dŠ, where F (x, y, z) = (y +29)î – xj + x³yk and S is the…

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Q: Use Stokes' theorem to evaluate Ĝ - dĩ, vhere Ĝ(1, Y, 2) = (2r, y,0) and D is any closed curve.

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Q: 2. For this entire page, let r(t) = (4 sin(t), 3t, 4 cos(t)) (a) Circle the correct graph for the…

A: The objective of this question is to understand the properties of the vector function r(t) = (4…

Q: Let fcxry)= 2X sinly)+3X Cos CY ). Find the tangent Plane at the point 2,0).Use the tangent Plane to…

A: In this question, concept of tangent plane at any point is applied. Tangent Plane Naturally, it…

Q: The curve y = sin(πz), with 0 ≤ z ≤ 2, on the yz-plane is revolved once about the z-axis. Find a…

A: Given that y=sin πz and 0≤z≤2 The objective is to find the vector equation. The image formed is like…

Q: Let ♬ =. Use Stokes' Theorem to evaluate So F. dr, where C is the curve of intersection of the…

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Q: a. Sketch the surface x2 - y2 + z2 = 4. b. Find a vector normal to the surface at (2, -3, 3). Add…

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Q: Use Stokes's theorem to evaluate OF.dr for the given F and C. (c) F(x, y, z) = xzi+ xyj– 3xz k, C :…

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Q: Consider surface S of the cone S : z = 2/a2+ y² at the point P(1, , V5). (a) Determine the vector…

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Q: Use Green's Theorem to evaluate fa F. dr where F(x, y) = (y cos x, x² + 2y sin x) and C is the…

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Q: Let r(t) = (et, et sin t, et cos t).  Find the equation of the plane that is normal to the curve at…

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Q: Let F = . [F Use Stokes' Theorem to evaluate F.dr, where C is the triangle with vertices (7,0,0),…

A: Given,             F→=4x+y2, 8y+z2, 9z+x2, Use Stokes' Theorem to find:                ∫CF→·dr→,…

Q: Use Stokes' Theorem to evaluate of intersection of the plane x + 3y +z = 12 with the coordinate…

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Q: П π Find T, N, and k for the plane curve r(t) = 7t i +7 In (cost) j. - <t<2.

A: Since you have uploaded multiple questions according to our guidelines we have solved first question…

Q: xỉ + yj+zk. If ū

A: In the given question, the concept of curl is applied. Curl Curl is a vector operator in…

Q: H.W Which of the following vectors is normal to the surface x?yz = 1 at (1,1,1)? (a) 4i +j+17k, (b)…

A: Given the surface is x2yz=1 and (x,y,z)=(1,1,1)

Q: Let Q be the rectangle formed by (0, 0, 0), (1, 0, 0), (0, 1, 1) and (1, 1, 1) oriented CCW as x² dx…

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Q: :) Use Stokes' theorem to evaluate RF dr where C F = z?i + yj + xk and C is the triangle with…

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Q: Let F = SOFF Use Stokes' Theorem to evaluate . dr, where C is the triangle with vertices (6,0,0),…

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Q: r = 14,0 = I 4 Description of locus in (x, y, z) space: Line made by the intersection of the…

A: Given the Polar coordinates      r=14 and θ=π4 Find the Cartesian coordinate y.

Q: F(x, y, z) = yzi + 8xzj + exyk, C is the circle x² + y² = 1, z = 4.

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Q: Let F = Use Stokes' Theorem to evaluate с شرح = F. dr, where C is the curve of intersection of the…

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Q: a. Find the normal vector to the tangent plane b. Find an equation of the tangent plane to the given…

A: What is Parametric Surface: The concept of parameterized curves is extended to vector-valued…