A particle moving in the xy plane experiences a velocity dependent force $\overrightarrow F = k\left( {{v_y}\widehat i + {v_x}\widehat j} \right)$ , where vx and vy are the x and y components of its velocity $\overrightarrow v $ . If $\overrightarrow a $ is the acceleration of the particle, then which of the following statements is true for the particle?

Question

A particle moving in the xy plane experiences a velocity dependent force
$\overrightarrow F = k\left( {{v_y}\widehat i + {v_x}\widehat j} \right)$ , where v_x and v_y are the
x and y components of its velocity $\overrightarrow v $ . If $\overrightarrow a $ is the
acceleration of the particle, then
which of the following statements is true for the particle?

kinetic energy of particle is constant in time

quantity $\overrightarrow v \times \overrightarrow a $ is constant in time

quantity $\overrightarrow v .\overrightarrow a $ is constant in time

$\overrightarrow F $ arises due to a magnetic field

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