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GATE 2023 MT – Question 40

Engineering Mathematics · Calculus and vector calculus · 2 marks · Multiple choice

A fluid flow has velocity $\mathbf V=e^{xyz}(x\hat i+z\hat k)$. Its curl at $(1,2,3)$ is

  1. $e^6(9\hat i-16\hat j-3\hat k)$
  2. $e^6(9\hat i-3\hat k)$
  3. $e^6(9\hat i+16\hat j-3\hat k)$
  4. $e^6(-16\hat i+9\hat j-3\hat k)$

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Correct answer: (A) $e^6(9\hat i-16\hat j-3\hat k)$

Explanation

Write $u=xe^{xyz},v=0,w=ze^{xyz}$. Curl is $(w_y,u_z-w_x,-u_y)=e^{xyz}(xz^2,y(x^2-z^2),-x^2z)$. At $(1,2,3)$, this becomes $e^6(9\hat i-16\hat j-3\hat k)$, **A**.