Suppose that F= -xyI -yzJ-xzK. Find the work done by this vector field on an object...

Suppose that F= -xyI -yzJ-xzK. Find the work done by this vector field on an object moving once counterclockwise (when viewed from above) around the path from (2,3,1) to (-4,6,2) to (1,-3,8) and back to (2,3,1). Solve using Stokes' theorem.

Expert Solution

milcah answered 3 years ago

Find the work done by the force field F in moving a particle through the path...

Find the work done by the force field F in moving a particle through the path C. That is, find Where C is the compound path given by r(t)=<t,0,t> from (0,0,0) to (2,0,2) followed by r(t)=<2,t,2> from (2,0,2) to (2,2,2)

Find the work done by the vector vield F(x, y) = 3x+3x2y, 3y2x+2x3 on a particle...

Find the work done by the vector vield F(x, y) = 3x+3x2y, 3y2x+2x3 on a particle moving first from (−3, 0), along the x-axis to (3, 0), and then returning along y = 9 − x2 back to the starting point.

(3) Let V be a vector space over a field F. Suppose that a ? F,...

(3) Let V be a vector space over a field F. Suppose that a ? F, v ? V and av = 0. Prove that a = 0 or v = 0. (4) Prove that for any field F, F is a vector space over F. (5) Prove that the set V = {a0 + a1x + a2x 2 + a3x 3 | a0, a1, a2, a3 ? R} of polynomials of degree ? 3 is a vector space over...

Let F be a vector field. Find the flux of F through the given surface. Assume...

Let F be a vector field. Find the flux of F through the given surface. Assume the surface S is oriented upward. F = eyi + exj + 24yk; S that portion of the plane x + y + z = 6 in the first octant.

Given the following vector force field, F, is conservative: F(x,y)=(2x2y4+x)i+(2x4y3+y)j, determine the work done subject to...

Given the following vector force field, F, is conservative: F(x,y)=(2x2y4+x)i+(2x4y3+y)j, determine the work done subject to the force while traveling along any piecewise smooth curve from (-2,1) to (-1,0)

Find the flux of the vector field F = x i + e2x j + z ...

Find the flux of the vector field F = x i + e2x j + z k through the surface S given by that portion of the plane 2x + y + 8z = 7 in the first octant, oriented upward.

Please show work and explain Prove that a vector space V over a field F is...

*Please show work and explain* Prove that a vector space V over a field F is isomorphic to the vector space L(F,V) of all linear maps from F to V.

Find the work done by the force field F(x,y) = <2xy-cosx,ln(xy)+cosy> along the path C, where...

Find the work done by the force field F(x,y) = <2xy-cosx,ln(xy)+cosy> along the path C, where C starts at (1,1)(1,1) and travels to (2,4)(2,4) along y=x^2, then travels down to (2,2)(2,2) along a straight path, and returns to (1,1)(1,1) along a straight path. Fully justify your solution.

Find the flux of the vector field F = (3x + 1, 2xe^z , 3y^2 z...

Find the flux of the vector field F = (3x + 1, 2xe^z , 3y^2 z + z^3 ) across the outward oriented faces of a cube without the front face at x = 2 and with vertices at (0,0,0), (2,0,0), (0,2,0) and (0,0,2).

Evaluate the surface integral S F · dS for the given vector field F and the...

Evaluate the surface integral S F · dS for the given vector field F and the oriented surface S. In other words, find the flux of F across S. For closed surfaces, use the positive (outward) orientation. F(x, y, z) = xy i + yz j + zx k S is the part of the paraboloid z = 6 − x2 − y2 that lies above the square 0 ≤ x ≤ 1, 0 ≤ y ≤ 1, and has...

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