## Question

###### 11. This problem is all about vector fields. The three parts are independent_Determine without searching for a potential function) whether the following vec- tor field is conservative. Your answer should be yes O no, followed by your (brief) reasoning: F = (z? yr ,y2 _ xy, 22 xy) (b) G = (2ry32' , 3x2y2 24 , 4x?y323 + 2) is a conservative vector field. Find the poten- tial function g(w,y, 2) such that 9(0,0,0) = 0. (c) h(x , Y,2) = 22 +y? + 22 is a potential function for conservative vecto

11. This problem is all about vector fields. The three parts are independent_ Determine without searching for a potential function) whether the following vec- tor field is conservative. Your answer should be yes O no, followed by your (brief) reasoning: F = (z? yr ,y2 _ xy, 22 xy) (b) G = (2ry32' , 3x2y2 24 , 4x?y323 + 2) is a conservative vector field. Find the poten- tial function g(w,y, 2) such that 9(0,0,0) = 0. (c) h(x , Y,2) = 22 +y? + 22 is a potential function for conservative vector field H = (2x,2y,22) . C is an unknown curve joining (0,0,0) to (1,2,3). Compute the work done in moving along C in the presence of H. 12 Consider the vector field F = (M,N,P) with M = y2? cos(zy) + In(2 + 1), N = rz? cos(ry) + 3 sin(2)eBysin(e) , P = 22 sin(ry) + + 3y cos( = 2)esy sin(e) 2 +1 Without finding the potential function; show that F is conservative. Find the potential function; 0, for the force. Evaluate J,1,o) (0,7/27) F dr