Allied & ICAR Exam Bank • ALLIED_2679 NAT • 2 Marks

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Divergence and curl

Question Statement:

If $\vec{F} = (a x + 3y)\hat{i} + (b y - z)\hat{j} + (x + c z)\hat{k}$ is solenoidal, and $a = 2, b = -5$, the value of $c$ must be:

Answer Key:

3

Step-by-Step Solution & Explanation

$\nabla \cdot \vec{F} = a + b + c = 0$. Given $a = 2, b = -5 \implies 2 - 5 + c = 0 \implies c = 3$.
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