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GATE 2025 ME – Question 13

Engineering Mathematics · Calculus: Gradient, divergence, curl, vector identities, line, surface and volume integrals · 1 mark · Multiple choice

The divergence of the curl of a vector field is

  1. the magnitude of this vector field
  2. the argument of this vector field
  3. the magnitude of the curl of this vector field
  4. zero

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Show answer and explanation

Correct answer: (D) zero

Explanation

The identity $\nabla \cdot (\nabla \times \vec{F}) = 0$ holds for every smooth vector field.