Physics Vectors & Equilibrium PMDC Conceptual Practice
PMDC Verified Question 13 of 50
If a force vector is given by \(\vec{F} = 2\hat{i} + 3\hat{j} - 4\hat{k}\) and the displacement vector is \(\vec{D} = \hat{i} - 2\hat{j} - 5\hat{k}\), calculate the work done by the force.
A
28 J
B
-24 J
C
-8 J
D
16 J
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option D: 16 J
Concept:
Work defined as the scalar (dot) product of force and displacement.

Formula:
$$W = \vec{F} \cdot \vec{D} = F_x D_x + F_y D_y + F_z D_z$$

Solution:
Substitute the components of the vectors into the formula:
$$W = (2)(1) + (3)(-2) + (-4)(-5)$$
$$W = 2 - 6 + 20$$
$$W = 16\text{ J}$$

Why other options are incorrect:
  • A, B, and C result from algebraic sign errors during multiplication (e.g., writing \((-4) \times (-5) = -20\) or incorrectly adding/subtracting the components).

Quality & Fidelity Assurance: Every question on BeambePrep is rigorously curated against the official PMDC syllabus with zero filler, zero out-of-syllabus content, and zero typos. When an authentic past paper originally contained a historical mistake or ambiguity from the examining board (such as UHS or NUMS), BeambePrep faithfully reflects the original paper while detailing the nuance and scientific consensus in the autopsy above.

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