GATE AG 2022 • Q18 NAT • 1 Mark

Section 1: Engineering Mathematics

Vector Calculus

Subtopic: Physical interpretations – line, surface and volume integrals

Question Statement:

Work done by a moving particle in the force field F̄ = 6x²î + (3xz + y)ĵ + 4zk̂, moving along the straight line from (0,0,0) to (1,2,3) is __________. [Answer in integer]

Official Answer Key:

28 to 28

Step-by-Step Solution & Explanation

• Parametrize x=t,y=2t,z=3t, t∈[0,1]: F̄·dr̄ = (24t²+40t)dt • W = ∫₀¹(24t²+40t)dt = 8+20 = 28 Computed value: W = 28 (exact match with official key)

Practice This in Real CBT Exam Interface

Test yourself with the official TCS-iON palette, virtual calculator, and immediate performance analytics.

Launch CBT Mock Test