For the work done to be 0, the particle should move in perpendicular direction to the application of force.
¯F=20^i+15^j
slope of F sF=1520
slope of the line is sl=−a3
if two lines are perpendicular product of their slopes is −1
hence, slsF=−1
⟹slsF=−a×154×20=−1
∴a=4