Allied & ICAR Exam Bank • ALLIED_0050 NAT • 2 Marks

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Vector differential operators – del, gradient

Question Statement:

The magnitude of the gradient of $\phi = x^2 + y^2 + z^2$ at the point $(1, 2, 2)$ is:

Answer Key:

6

Step-by-Step Solution & Explanation

$\nabla \phi = 2x\hat{i} + 2y\hat{j} + 2z\hat{k} = 2\hat{i} + 4\hat{j} + 4\hat{k}$. $|\nabla \phi| = \sqrt{2^2 + 4^2 + 4^2} = \sqrt{4 + 16 + 16} = \sqrt{36} = 6$.
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