Home › Previous year questions › GATE 2017 ME (ME1) › Question 37GATE 2017 ME (ME1) – Question 37 Engineering Mathematics · Calculus: Gradient, divergence, curl, vector identities, line, surface and volume integrals · 2 marks · Numerical answer
For $\mathbf V=2yz\hat{\mathbf i}+3xz\hat{\mathbf j}+4xy\hat{\mathbf k}$, find $\nabla\cdot(\nabla\times\mathbf V)$.
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Show answer and explanation Correct answer: 0 to 0
Explanation The divergence of a curl vanishes for a smooth vector field. A direct calculation gives $\nabla\times\mathbf V=(4x-3x,2y-4y,3z-2z)=(x,-2y,z)$. Its divergence is $1-2+1=0$, confirming the result without relying only on the identity.
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