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

Step-by-step solution

Work done by a constant force F d , where d = r _Q - r _P is the displacement. Given r _P = (3 i + 4 j + 5 k ) m and r _Q = (2 i + 3 j + 4 k ) m , the displacement is d = (2-3) i + (3-4) j + (4-5) k = (- i - j - k ) m . With F = (3 i + 4 j + 5 k ) N , the work done is W = F d = (3)(-1) + (4)(-1) + (5)(-1) = -12 ~J . The work done is -12 ~J .