Allied & ICAR Exam Bank • ALLIED_2673 MCQ • 1 Mark

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Vector differential operators – del, gradient

Question Statement:

If $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$ with $r = |\vec{r}|$, then $\nabla(r)$ equals:

Options:

  • (A) $\frac{\vec{r}}{r}$
  • (B) $r \vec{r}$
  • (C) $\vec{r}$
  • (D) $0$

Answer Key:

A

Step-by-Step Solution & Explanation

$\nabla(r) = \frac{\partial r}{\partial x}\hat{i} + \frac{\partial r}{\partial y}\hat{j} + \frac{\partial r}{\partial z}\hat{k} = \frac{x}{r}\hat{i} + \frac{y}{r}\hat{j} + \frac{z}{r}\hat{k} = \frac{\vec{r}}{r} = \hat{r}$.
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