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The gradient operator applied to a scalar yields a vector, and the divergence applied to a vector yields

  • A.a scalar in Cartesian coordinates but a vector in curvilinear ones
  • B.a second rank quantity requiring nine components to describe
  • C.a scalar
  • D.a vector

Answer: C

The three operations differ in what they take and what they return: gradient turns a scalar into a vector, divergence turns a vector into a scalar, and curl turns a vector into a vector. Keeping that straight prevents most sign and dimension errors.

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