Are acting on particle and displaced it from the point
2018
Forces 4î − 3ĵ + 7k̂ and −2î + 2ĵ − 8k̂ are acting on a particle and displace it from the point (5, 7, 1) to (2, 5, −6). The work done by the resultant force is:
Answer: C. 3 — ConceptWhen several forces act together, the net effect is their vector sum (the resultant). The work done by a force over a straight-line displacement equals…
- A.
25
- B.
9
- C.
3
- D.
7
Attempted by 2 students.
Show answer & explanation
Correct answer: C
Concept
When several forces act together, the net effect is their vector sum (the resultant). The work done by a force over a straight-line displacement equals the dot product of the force with the displacement vector: W = F · d. The displacement is always taken as (final position − initial position).
Application
Resultant force: add the two forces component-wise → F = (4 + (−2))î + (−3 + 2)ĵ + (7 + (−8))k̂ = 2î − ĵ − k̂.
Displacement: d = (final − initial) = (2 − 5)î + (5 − 7)ĵ + (−6 − 1)k̂ = −3î − 2ĵ − 7k̂.
Dot product, term by term: W = (2)(−3) + (−1)(−2) + (−1)(−7) = −6 + 2 + 7.
Sum the signed terms: W = 3 units.
Cross-check
Watch the signs: only one of the three products is negative (−6), while the other two are positive (+2 and +7). Keeping each sign gives −6 + 2 + 7 = 3, confirming the result. Dropping a sign or summing magnitudes would change the answer, so each component sign must be preserved.