A particle is subjected to forces P = 2i − 5j + 6k and Q = −i + 2j − k. The positional vectors are OA = 4i − 3j − 2k and OB = 6i + j − 3k. Work done by the resultant force (F = P + Q) to move the particle from A to B is
Reconstruction of the vector diagram given with AG Q.27 — position vectors OA and OB from origin O and the displacement AB.
Options:
(A) 2
(B) −5
(C) 12
(D) −15
Official Answer Key:
D
Step-by-Step Solution & Explanation
Resultant force: F = P + Q = (2−1)i + (−5+2)j + (6−1)k = i − 3j + 5k.
Displacement: d = AB = OB − OA = (6−4)i + (1+3)j + (−3+2)k = 2i + 4j − k.
W = F · d = (1)(2) + (−3)(4) + (5)(−1) = 2 − 12 − 5 = −15 units.
Distractor (C) 12 comes from taking the magnitude of the middle term only; (A) 2 from using OA·OB-type shortcuts.
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