Use Stoke's Theorem to find the work done by the force field F(x, y, z) = (esin x + 2y², 6x + tan- y, xz) in moving a particle one time along the positively oriented triangle with vertices at (2,0,0), (0,1,0) and (0,0,2).
Q: Use Stoke's Theorem to find the work done by the force field F(x, y, z) = (ein z + 2y², 6x + tan¬1…
A: Given force field is F→(x,y,z)=esinx+2y2, 6x+tan-1y, xz Now, we will find the Curl(F→).…
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A: As per guidelines, we will solve the first question only.
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- Find the work done by a force F = 6ỉ + 57– 3k when a particle moves from point | P(-3, 4, 5) to point Q(2, -3, -1) in space.Find the work done by the force field 2 2, , , 3 , x y z z z y z z x F in moving a particle along the line segment from (0, 2, 0) to (−4, 3, 2).Evaluate The Work Done By The Force Vector, F= (6x^2+3y)I – 15yzj + 10x^2zk From (0,0,0) To (1,1,1) Along The ff Paths In Space. a.the curve defined by the following parametric equations x=t y=t^2 z=t^2 b.straight lines from (0,0,0) to (1,0,0) then to (1,1,1) c. the straight line joining (0,0,0) and (1,1,1)
- The work done by the vector field F(x, y) = (-y², ²) along the arc of the parabola y = 2x² - 4x + 2 from the point (1,0) to the point (0, 2) followed by the line segment from the point (0, 2) to the point (-1,2) equals: O a. 6/55 O b. 77/15 O c. None of these. O d. 55/13 O e. 55/17 Check cross out cross out cross out cross out cross outExpress the vector field B = (x^2- y^2)ay + xzaz in spherical coordinates at ( 4, 30o, 120o) * Express the vector field B = (x2 – y²)ay + xza, in spherical coordinates at ( 4, 30°, 120°) 6.78ar + 0.232ae + 9aØ -3.87ar - 0.332ae + 5aØ -9.87ar + 0.232ae + 6aØ O -3.87ar + 0.232ae + aØFind the work done by the force field F in moving an object from P(-7, 7) to Q(7,5). F(x, y)
- Use Green's theorem to calculate the work done by the force F(x, y) = xy'i + 3x?yj on a particle that is moving counterclockwise around the triangle with vertices (-3, 0), (0, 0), and (0, 3).10) Use Green's Theorem to find the work done by the force field F(r,y) iiyjim moving a particle starting at the point (1,0), mOving up And to the left along the circle /-1 unfi the point (,0), and finally moving right along the xis back to the point (1,0),