X 20. Consider the vector field F x/ 3 where x denotes the vector xi + yj + zk = (x, y, z). Which of
X 20. Consider the vector field F x/ 3 where x denotes the vector xi + yj + zk = (x, y, z). Which of the following are true? (i) div(F) = 0 on its maximal domain of definition. (ii) curl(F) = 0 on its maximal domain of definition. (ii) F . dS = 0 for any closed surface on which F is defined. S (iv) /F . dr = 0 on any simple, closed, smooth curve on which F is defined. C
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