A 1 kg block subjected to two simultaneous forces (2 i + 3 j + 4 k ) N and (3 i - j - 2 k ) N is moved a distance of 25 m along (3 i - 4 j ) direction. The work done in this process is _____ J.

Step-by-step solution

The net force acting on the block is the vector sum of the two forces: F = F ₁ + F ₂ = (2 i + 3 j + 4 k ) + (3 i - j - 2 k ) = 5 i + 2 j + 2 k N The block is moved a distance of 25 m along the direction of the vector 3 i - 4 j . The unit vector along this direction is: n = 3 i - 4 j 3^2 + (-4)^2 = 3 i - 4 j 5 The displacement vector s is the magnitude multiplied by the unit vector: s = 25 n = 25 ( 3 i - 4 j 5 ) = 15 i - 20 j m The work done W is the dot product of the net force and the displacement vector: W = F s