Allied & ICAR Exam Bank • ALLIED_0783 MCQ • 1 Mark

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Vector differential operators – del, gradient

Question Statement:

A vector field $\vec{F}$ is said to be irrotational if:

Options:

  • (A) $\nabla \times \vec{F} = 0$
  • (B) $\nabla \cdot \vec{F} = 0$
  • (C) $\vec{F} = 0$
  • (D) $\nabla (\nabla \cdot \vec{F}) = 0$

Answer Key:

A

Step-by-Step Solution & Explanation

An irrotational vector field has zero curl: $\nabla \times \vec{F} = 0$, implying it can be represented as the gradient of a scalar potential $\vec{F} = \nabla \phi$.
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