A particle is displaced from point P ( 3 m , 4 m , 5 m ) to a point Q ( 2 m , 3 m , 4 m ) under a constant force F = ( 3 i ^ + 4 j ^ + 5 k ^ ) N . The work done by the force in this process is

Question

A particle is displaced from point P ( 3 m , 4 m , 5 m ) to a point Q ( 2 m , 3 m , 4 m ) under a constant force F = ( 3 i ^ + 4 j ^ ​ + 5 k ^ ) N . The work done by the force in this process is

TestHub · Accepted Answer

Initial position vector r 1 ​ = 3 i ^ + 4 j ^ ​ + 5 k ^ Final position vector r 2 ​ = 2 i ^ + 3 j ^ ​ + 4 k ^ Displacement vector s = r 2 ​ − r 1 ​ = ( 2 − 3 ) i ^ + ( 3 − 4 ) j ^ ​ + ( 4 − 5 ) k ^ = − i ^ − j ^ ​ − k ^ Force F = 3 i ^ + 4 j ^ ​ + 5 k ^ Work done W = F ⋅ s = ( 3 i ^ + 4 j ^ ​ + 5 k ^ ) ⋅ ( − i ^ − j ^ ​ − k ^ ) W = 3 ( − 1 ) + 4 ( − 1 ) + 5 ( − 1 ) = − 3 − 4 − 5 = − 12 J Answer: − 12 J

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