A force F = -K(yi→+xj→) (where K is a positive constant) acts on a particle moving in the xy-plane. Starting from the origin, the particle is taken along the positive x-axis to the point (a, a). The total work done by the force F on the particles.

While moving from (0, 0) to (a, 0)Along positive x-axis, y = 0      F→  = -kxj→i.e. force in negative y-direction while displacement is in positive x-direction.W1= 0Because force is perpendicular to displacementThen particle moves from (a, 0) to (a, a) along a line parallel to y-axis (x = +a) during this F→ = -k(yi→+aj→)The first component of force, -kyi→  will not contribute any work because this component is along negative x-direction (-i→) while displacement is in positive y-direction (a, 0) to (a, a). The second component of force i.e. -kaj→ will perform negative workW2 = (-kaj→).(aj→) = (-ka)(a)   = -ka2So net work done on the particle W = W1 +W2= 0 +(-ka2)  = -ka2