Use Stokes' Theorem to find the circulation of F = 4yi +7zj +3ck around the triangle C' obtained by tracing out the path (5, 0, 0) to (5, 0, 5), to (5, 4, 5) back to (5, 0, 0). Circulation = F. dr = C

Q: A force F = -3i +j+6k acts through the point (5,-2,-1). Find its moment about the point (3,0,2).

A: Moment of force about the point is given by cross product of position vector r about a point and…

Q: 2 = 8 at the

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Q: A particle moves along line segments from the origin to the points (2, 0, 0), (2, 3, 1), (0, 3, 1),…

A: Given that a particle moves along line segments from the origin to the points (2, 0, 0), (2, 3, 1),…

Q: H=pz Csup ap te'sin dg tpan 2 At point (1, ,6)

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Q: Use Stokes' Theorem to find the circulation of F = 4yi + 4zj+ 3xk around the triangle obtained by…

A: We have to find ∫CF→·dr→ using Stokes'sTheorem

Q: Find a vector tangent to the curve of intersection of the two cyclinders x2+y2=32x2+y2=32 and…

A: Solution: The objective is to find a vector tangent to the curve of intersection of the two…

Q: Determine the parametric equations of the flow lines for the velocity vector field, v, where v =…

A: The given velocity vector is v=yi+xj. To Find: parametric equations for flow lines of the above…

Q: F• dr where C is oriented counterclockwise as viewed from above. Jc Use Stokes' Theorem to evaluate…

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Q: divE = 0 divĦ = 0 curlĒ = %3| c Ət 1 DỂ curlĦ Using Maxwell's equations, show (V· V)Ē : c2 Ət?

A: Given:  ∇E=0∇H=0∇×E=-1c∂H∂t∇×H=1c∂E∂t

Q: Example Let f(r,y, z) = ryz sin rz. Find Vfo at the point Po = (1, –2, 7) and compute the…

A: to find : (1) grad f. (2) directional derivative.

Q: Find the Jacobian w/ respect to UVW X=U(3-v), Y= uv(3-w), Z=Uw

A: Our aim is to find the jacobian of x=u(3-v), y=uv(3-w) and z=uvw⇒x=3u-uv ,   y=3uv-uvw and…

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: Use Stokes' Theorem to find the circulation of F = 5yi + 3zj + 6xk around a circle C of radius 7…

A: Stokes' Theorem: The formula for Stokes' Theorem is given by:         ∫CF→·dr=∬RCurl F→·n→ dA where…

Q: oss product (i+ ej +e-k} × (2i + e'j -

A: We have to find the cross product according to the given vector

Q: The normal vector to the tangent plane for the surface x²y³ z = 8, at the point (-1, 2, 1) is: 2 3…

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Q: Find a Vector ū: non zero Vector perpendicular to the

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Q: Use Stokes' Theorem to find the circulation of F= 2yi +423 +3ack around the triangle obtained by…

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Q: The unit normal vector to the surface x'y + 2xz? = 8 at the point %3D (1,0, 2) is

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Q: Use Stokes' Theorem to find the circulation of F = 2yi + 3zj + 7xk around the triangle obtained by…

A: Here we have to solve the given problem using stokes' theorem.

Q: Evaluate the circulation of G = ayi+zj+ 7yk around a square of side 9, centered at the origin, lying…

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Q: Compute the integral of ſA° · dľ°P2P1 from point P1 (2,1, -1) to P2 (8,2, -1) of the vector function…

A: We have to find the integral from point p1 TP p2.

Q: Let f(x, y) = xe*²-v' and P = (1, 1). Find the rate of change of f in the direction of a vector…

A: The given problem is to find the rate of change of given function f in the direction of a vector…

Q: The velocity field for a flow is given by V = ut + vj + wk where u = 3x, y = -2y and w = 2z. Find…

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Q: In spherical coordinates, (r, 0, ø), the gradient takes the form 1df 1 ðf Vf (r, 0, ø) : -î + -0 +…

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Q: Use Stokes' Theorem to find the circulation of F = 3yi + 2zj + 2xk around the triangle obtained by…

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