The function \(\varphi(x, y, z)\) = xy + yz + az is a potential for the vector field \(\vec{F}\) =

(A) \((y+z) \hat{i}+(x+z) \hat{j}+(x+y) \hat{k}\)

(B) \((x+y) \hat{i}+(y+z) \hat{j}+(x+z) \hat{k}\)

(C) \((x+z) \hat{i}+(x+y) \hat{j}+(y+z) \hat{k}\)

Choose the correct answer from the options given below: