$A$ particle of mass $m$ and charge $q$ is thrown from the origin at $t = 0$ with velocity $\vec{v} = 2\hat{i} + 3\hat{j} + 4\hat{k}$ units in a region with a uniform magnetic field $\vec{B} = 2\hat{i}$ units. After time $t = \frac{\pi m}{qB}$,an electric field $\vec{E}$ is switched on such that the particle moves in a straight line with constant speed. $\vec{E}$ may be:

  • A
    $5\hat{k} - 10\hat{j}$ units
  • B
    $-6\hat{k} - 9\hat{j}$ units
  • C
    $-6\hat{k} + 8\hat{j}$ units
  • D
    $6\hat{k} + 8\hat{j}$ units

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