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Consider the following statements about the del operator.

1. The curl of a gradient is zero   2. The divergence of a curl is zero   3. The gradient of a divergence is zero

  • A.2 and 3 only are correct
  • B.1 and 3 only are correct
  • C.1 and 2 only are correct
  • D.1, 2 and 3 are all correct identities of vector calculus

Answer: C

The first two are genuine identities and both are used constantly in field theory. The third is not an identity at all: the gradient of a divergence is a perfectly good non-zero vector, and it appears in the expansion of the curl of a curl.

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