Allied & ICAR Exam Bank • ALLIED_0057 MCQ • 1 Mark

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Divergence and curl

Question Statement:

The curl of the position vector $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$ is:

Options:

  • (A) $\vec{0}$
  • (B) $3\hat{k}$
  • (C) $\hat{i} + \hat{j} + \hat{k}$
  • (D) $\vec{r}$

Answer Key:

A

Step-by-Step Solution & Explanation

$\nabla \times \vec{r} = \begin{vmatrix} \hat{i} & \hat{j} & \hat{k} \\ \partial/\partial x & \partial/\partial y & \partial/\partial z \\ x & y & z \end{vmatrix} = \vec{0}$.
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