A force \( F=-K(\hat{y i+}+x \hat{j}) \) (where \( K \) is a positive constant) acts on a partic...

A force \( F=-K(\hat{y i+}+x \hat{j}) \) (where \( K \) is a positive constant) acts on a particle moving in the \( x y \)-plane. Starting from the origin, the particle is taken along the positive \( x \)-axis to the point \( (a, 0) \) and then parallel to the \( y \)-axis to the point \( (a, a) \). The total work done by the force \( F \) on the particles is