A particle moving in the xy plane experiences a velocity dependent force \(\vec F = k(v_y \hat i + v_x \hat j)\), where vx and vy are the x and y components of its velocity \(\bar v\). If \(\bar a\) is the acceleration of the particle, then which of the following statements is true for the particle?
(1) Quantity \(\vec v.\vec a\)is constant in time
(2) Kinetic energy of particle is constant in time
(3) Quantity \(\vec v \times \vec a\) is constant in time
(4) \(\vec F\) arises due to a magnetic field