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GATE 2024 MN – Question 26

Engineering Mathematics · Vector Calculus · 1 mark · Multiple choice

Find $|\nabla\times\mathbf F|$ for $\mathbf F=2x\mathbf i+3y\mathbf j+4z\mathbf k$.

  1. 0
  2. 4
  3. 9
  4. 25

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Correct answer: (A) 0

Explanation

Each component depends only on its own coordinate. All cross-coordinate derivatives in the curl are therefore zero, so the curl vector and its magnitude are 0, A. The nonzero divergence 2+3+4=9 is a different vector-calculus operation.

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