Allied & ICAR Exam Bank • ALLIED_2677 NAT • 2 Marks

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Divergence and curl

Question Statement:

For the position vector $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$ in three dimensions, the value of $\nabla \cdot \vec{r}$ is:

Answer Key:

3

Step-by-Step Solution & Explanation

$\nabla \cdot \vec{r} = \frac{\partial x}{\partial x} + \frac{\partial y}{\partial y} + \frac{\partial z}{\partial z} = 1 + 1 + 1 = 3$.
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