Question Bank • QB_EM_103 NAT • 2 Marks

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Scalar and vector point functions

Question Statement:

If $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$ and $r = |\vec{r}|$, calculate the value of $\nabla \cdot \vec{r}$.

Answer Key:

3

Step-by-Step Solution & Explanation

$\nabla \cdot \vec{r} = \frac{\partial x}{\partial x} + \frac{\partial y}{\partial y} + \frac{\partial z}{\partial z} = 1 + 1 + 1 = 3.0$
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