Allied & ICAR Exam Bank • ALLIED_0054 MCQ • 1 Mark

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Divergence and curl

Question Statement:

For any twice continuously differentiable vector field $\vec{A}$, $\nabla \cdot (\nabla \times \vec{A})$ is identically:

Options:

  • (A) $0$
  • (B) $\nabla^2 \vec{A}$
  • (C) $\vec{A}$
  • (D) $-1$

Answer Key:

A

Step-by-Step Solution & Explanation

The divergence of any curl field is identically zero: $\text{div}(\text{curl } \vec{A}) = 0$.
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