(1 point) Are the following statements true or false? I. If F = Vf, then F is co
ID: 3144461 • Letter: #
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(1 point) Are the following statements true or false? I. If F = Vf, then F is conservative. 2. If F is path-independent and C is any closed curve, then fc F·dF = 0. 3. If the vector fields F and G have Fi G di for a particular path C, then F=G. 4. lffcF-dr = 0 for one particular closed path, then F is path-independent. 5. If F is path-independent, then there is a potential function for F. 6. If // F . dr 0 for some closed path C, then F is path dependent. 7. IgE . dr = f(O)-f(P) whenever P and Q are the endpoints of the curve C.Explanation / Answer
A) False as when gradf is 0 then it is conservative.
B) true as when the path is closed , initial and end point is same hence the integral is 0.
C) False as there may be two different paths having the same integral as x^2 and x/3 taken from 0 to 1 give same value.
D) True as if is 0 for one path it is path independent.
E) True
F) False as it may be path independenr if 0 on some other path .
G) true , as if P and Q are the end points then integral is given by thw difference of its values at end points
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