Allied & ICAR Exam Bank • ALLIED_2674 NAT • 1 Mark

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Vector differential operators – del, gradient

Question Statement:

If $\vec{r} = x\hat{i} + y\hat{j} + z\hat{k}$, then $\nabla(r^2)$ equals $k \vec{r}$. The value of $k$ is:

Answer Key:

2

Step-by-Step Solution & Explanation

$r^2 = x^2 + y^2 + z^2$. $\nabla(r^2) = 2x\hat{i} + 2y\hat{j} + 2z\hat{k} = 2\vec{r}$. Hence $k = 2$.
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