A uniform force of (3î + ĵ) newton acts on a

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A uniform force of (3î + ĵ) newton acts on a particle of mass 2 kg. the particle is displaced from position (2î + k̂) meter to position (4î + 3ĵ - k̂) meter. The work done by the force on the particle is

1. 6 J
2. 13 J
3. 15 J
4. 9 J

Correct Option: D

Given : F^{^→} = 3î + ĵ
r₁^{^→} = (2î + k̂) , r₂^{^→} = (4î + 3ĵ - k̂)
r^{^→} = r₂^{^→} - r₁^{^→} = (4î + 3ĵ - k̂) - (2î + k̂)
or r^{^→} = 2î + 3ĵ - 2k̂
so work done by the given force w = F^{^→} . r^{^→}
= (3î + ĵ) . (2î + 3ĵ - 2k̂) = 6 + 3 = 9 J