GATE AG 2010 • Q26 MCQ • 1 Mark

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Divergence and curl

Question Statement:

The curl of the vector A = xy i + yz j + zx k is

Options:

  • (A) xi+yj+zk
  • (B) −xi−yj−zk
  • (C) yi+zj+xk
  • (D) −yi−zj−xk

Official Answer Key:

D

Step-by-Step Solution & Explanation

curl A = |i j k; ∂/∂x ∂/∂y ∂/∂z; xy yz zx|. i-component: ∂(zx)/∂y − ∂(yz)/∂z = 0 − y = −y. j-component: ∂(xy)/∂z − ∂(zx)/∂x = 0 − z = −z. k-component: ∂(yz)/∂x − ∂(xy)/∂y = 0 − x = −x. curl A = −y i − z j − x k.

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