Question Bank • QB_SUB_EM_0076 NAT • 2 Marks

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Vector differentiation

Question Statement:

For the vector field $\vec{F} = (2x + y)\hat{i} + (3y - z)\hat{j} + (4z + x)\hat{k}$, the divergence $\nabla \cdot \vec{F}$ is:

Answer Key:

9.0

Step-by-Step Solution & Explanation

$\nabla \cdot \vec{F} = \frac{\partial}{\partial x}(2x + y) + \frac{\partial}{\partial y}(3y - z) + \frac{\partial}{\partial z}(4z + x) = 2 + 3 + 4 = 9.00$
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