Question: The force exerted by an electric charge at the origin on a charged particle at a point (X, y, z) with position vector r =

field is not conservative, enter DNE.) F ( x, y) = (7x6

The force exerted by an electric charge at the origin on a charged particle at a point (X, y, z) with position vector r = (x, y, z) is F(r) = Kr/Irl 3 where K is a constant. Find the work done as the particle moves along a straight line from (5, O, 0) to (5, 2, 5). Determine whether or not F is a conservative vector field. If it is, find a function f such that F = Vf. (If the vector field is not conservative, enter DNE.) F ( x, y) = (7x6 y + y- 4)i+ (x7 - 4xy - 5) j, y>o f ( x, y ) =Consider F and C below. F(x, y) = (4 + 2xy-)i+ 2x2yj, C is the arc of the hyperbola y = _ from (1, 1) to(4, X (a) Find a function f such that F = Vf. f ( x, y ) = (b) Use part (a) to evaluate F . dr along the given curve C. CFind the work done by the force field F in moving an object from P to Q. F(X, y) = (2X + y)i + Xj; P(1, 1), Q(6, 2)

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