(a) Torque due to weight of coil,
`vectau=(a/2 hati)xx(-mghatk)=mga/2(hatj)`
For the equilibrium of loop, torque on it must be along negative y-axis. Let the magnetic moment of loop be `mu hat k`.As the loop lies in x-y plane, its magnetic moment vector (from right hand thumb rule) either points up or down.
Torque due to magnetic force, `vectau_B =vec mu xx vec B = mu hat k xx (3hat i+4hat k)B_0 = 3muB_0hat j`
If it is in negative direction, `vec mu` must point downward. So, the current in the coil must be from P to Q.
(b) Force acting on arm
`RS=I(vec I xx vec B)=I[(-bhatj)xx(3hati+4hatk)B_0]`
`=IB_0b(3hatk-4hatj)`
(c) In equilibrium `vectau_(gravity)+vec tau_B=0`
Hence, `3(abI)B_0=(mga)/2` or `I=(mg)/(6B_0b)`.