Question Detail
Question
A body moves from position r₁ = -2i + 3j + k (m) to r₂ = 3i - 2j - k (m) under a force F = 2i - 3j - k (N). What is the work done?
Correct Answer
Option A is the correct answer.
Detailed Explanation
First, find the displacement vector: Δr = r₂ - r₁ = (3-(-2))i + (-2-3)j + (-1-1)k = 5i -5j -2k. Work done W = F · Δr = (2)(5) + (-3)(-5) + (-1)(-2) = 10 + 15 + 2 = 27 J.
Hint
Work done by a constant force is the dot product of the force vector and the displacement vector.