Physics Vectors & Equilibrium PMDC Conceptual Practice
PMDC Verified Question 39 of 50
Find the work done in moving an object along a straight line from position \( (3, 2, -1) \) to position \( (2, -1, 4) \) under a force field given by \(\vec{F} = 4\hat{i} - 3\hat{j} + 2\hat{k}\).
A
10 J
B
12 J
C
15 J
D
17 J
Tap any option to test your recall and reveal the step-by-step Propolis autopsy.

Propolis Cognitive Error Autopsy

Official Correct Choice:
Option C: 15 J
Concept:
Calculating work done between two spatial coordinates.

Formula:
$$\vec{d} = (x_2 - x_1)\hat{i} + (y_2 - y_1)\hat{j} + (z_2 - z_1)\hat{k}$$
$$W = \vec{F} \cdot \vec{d}$$

Solution:
Step 1: Calculate the displacement vector \(\vec{d}\):
$$\vec{d} = (2 - 3)\hat{i} + (-1 - 2)\hat{j} + (4 - (-1))\hat{k}$$
$$\vec{d} = -\hat{i} - 3\hat{j} + 5\hat{k}$$
Step 2: Calculate the dot product:
$$W = (4)(-1) + (-3)(-3) + (2)(5)$$
$$W = -4 + 9 + 10$$
$$W = 15\text{ J}$$

Why other options are incorrect:
  • A, B, and D result from arithmetic mistakes such as writing \(4 - (-1) = 3\) or failing to include the negative sign for the first component.

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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