Please help with problem both a and b!!! For a i have xyz^2-yz+c, i do not know if this is correct and if so I do not know how to proceed with part b. Please any advise is appreciated!!

a. Find a potential function for F(x,y,z)=⟨yz^2 ,xz^2 −z,2xyz−y⟩.
b. Use part (a) to evaluate ∫c F*ds where C is any path in space from P = (1,2,3) to Q = (3,2,1).

Question

Please help with problem both a and b!!! For a i have xyz^2-yz+c, i do not know if this is correct and if so I do not know how to proceed with part b. Please any advise is appreciated!!

a. Find a potential function for F(x,y,z)=⟨yz^2 ,xz^2 −z,2xyz−y⟩.
b. Use part (a) to evaluate ∫c F*ds where C is any path in space from P = (1,2,3) to Q = (3,2,1).

anonymous · Answer

a. Yes, f(x,y,z)= xyz^2-yz+c is a potential function for the F(x,y,z) vector field.
b. Because a potential function exists, it means that the vector field is conservative and its integral on any path  from P to Q will have the same value w=f(Q)-f(P), note that the constant c will cancel. Using the numerical values, w=4-12=-8.