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GATE 2023 CH – Question 12

Engineering Mathematics · Calculus: Gradient, divergence, curl, vector identities and integral theorems · 1 mark · Multiple choice

The vector $\vec{v}$ is defined as $\vec{v} = zx\hat{i} + 2xy\hat{j} + 3yz\hat{k}$. Which one of the following is the CORRECT value of divergence of $\vec{v}$, evaluated at the point $(x, y, z) = (3, 2, 1)$ ?

  1. 0
  2. 3
  3. 14
  4. 13

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Correct answer: (D) 13

Explanation

$\nabla \cdot \vec{v} = \frac{\partial(zx)}{\partial x} + \frac{\partial(2xy)}{\partial y} + \frac{\partial(3yz)}{\partial z} = z + 2x + 3y = 1 + 6 + 6 = 13$.