Three forces, (15i + j) N, (5qi – pj) N and (–3pi – qj) N, where p and q are constants, act on a particle. Given that the particle is in equilibrium, find the value of p and the value of q. (Mechanics 1 June 2017)

As the particle is at rest, the net force acting on the particle must be equal to zero, i.e. Fres = 0Therefore, (15i + j) + (5qi - pj) + (-3pi - qj) = 0Collating 'i' terms: 15 + 5q - 3p = 0 (Equation 1)Collating 'j' terms: 1 - p - q = 0 (Equation 2) p = 1-qSubsitute 'p' into Equation 1:15 + 5q - 3(1 - q) = 0Expanding the bracket: 15 + 5q - 3 + 3q = 0Collate terms:12 + 8q = 0 Make 'q' the subject:q = -12/8 = -3/2 (or -1.5)Substituting 'q' to find 'p':p = 1 - (-3/2) = 5/2 (or 2.5)