A particle moving in the xy plane experiences a velocity dependent force \vec{F}=k\left ( v_{y}\hat{i}+v_{x}\hat{j} \right ), where v_{x}\; \; and\; \; v_{y} are the x and y components of its velocity \vec{v}. If \vec{a} is the acceleration of the particle, then which of the following statements is true for the particle ?
Option: 1 quantity \overrightarrow{v}\times\overrightarrow{a} is constant in time
 
Option: 2 \overrightarrow{F} arises due to a magnetic field
Option: 3 Kinetic energy of particle is constant in time  
Option: 4 quantity \overrightarrow{v}.\overrightarrow{a} is constant in time

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