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#Engineering

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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