Allied & ICAR Exam Bank • ALLIED_2669 MCQ • 1 Mark

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Vector differentiation

Question Statement:

The gradient of a scalar field $\phi(x, y, z)$ at any point is a vector that points in the direction of:

Options:

  • (A) Maximum rate of increase of $\phi$
  • (B) Minimum rate of increase of $\phi$
  • (C) Zero change in $\phi$
  • (D) Opposite to the level surface

Answer Key:

A

Step-by-Step Solution & Explanation

$\nabla \phi$ points in the direction of the steepest ascent (maximum rate of increase), and its magnitude equals this maximum rate.
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