Allied & ICAR Exam Bank • ALLIED_0058 NAT • 2 Marks

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Vector differential operators – del, gradient

Question Statement:

If $\phi(x, y, z) = x y z$, the value of $\nabla^2 \phi$ at $(1, 2, 3)$ is:

Answer Key:

0

Step-by-Step Solution & Explanation

$\nabla^2 \phi = \frac{\partial^2(xyz)}{\partial x^2} + \frac{\partial^2(xyz)}{\partial y^2} + \frac{\partial^2(xyz)}{\partial z^2} = 0 + 0 + 0 = 0$.
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