A particle moves from an initial point A(1, 2, -1) m to a final point B(x, 4, 2) m under the influence of a constant force F = (3 i - 2 j + 4 k ) N. If the total work done by the force is 14 J, the value of the coordinate x is:

Step-by-step solution

The displacement vector s of the particle is given by the difference between the final and initial position vectors: s = r _B - r _A s = (x - 1) i + (4 - 2) j + (2 - (-1)) k s = (x - 1) i + 2 j + 3 k m The work done W by a constant force is the dot product of the force and displacement vectors: W = F s W = (3 i - 2 j + 4 k ) ((x - 1) i + 2 j + 3 k ) W = 3(x - 1) + (-2)(2) + (4)(3) W = 3x - 3 - 4 + 12 W = 3x + 5 Given that the total work done is 14 J: 3x + 5 = 14 3x = 9 x = 3 Answer: 3