Allied & ICAR Exam Bank • ALLIED_0049
NAT • 2 Marks
Section 1: Engineering Mathematics
Vector Calculus
Subtopic: Divergence and curl
Question Statement:
The divergence of the vector field $\vec{V} = (x^2 y)\hat{i} + (y^2 z)\hat{j} + (z^2 x)\hat{k}$ at the point $(1, 2, 3)$ is:
Step-by-Step Solution & Explanation
$\nabla \cdot \vec{V} = \frac{\partial}{\partial x}(x^2 y) + \frac{\partial}{\partial y}(y^2 z) + \frac{\partial}{\partial z}(z^2 x) = 2xy + 2yz + 2zx$. At $(1, 2, 3)$: $2(1)(2) + 2(2)(3) + 2(3)(1) = 4 + 12 + 6 = 22$. Wait, $4 + 12 + 6 = 22$. So value is 22.
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