Question Bank • QB_EM_147 NAT • 1 Mark

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Divergence and curl

Question Statement:

For the position vector $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$, calculate the divergence $\nabla \cdot \vec{r}$.

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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