A particle of mass \( m \) is moving in the \( xy \)-plane such that its velocity at a point \( (x, y) \) is given as \( \vec{v} = \alpha(y\hat{x} + 2x\hat{y}) \), where \( \alpha \) is a non-zero constant. What is the force \( \vec{F} \) acting on the particle?
