In a certain region static electric and magnetic fields exist. The magnetic field is given by $\overrightarrow{B} = B_0 (\hat{i} + 2 \hat{j} - 4 \hat{k})$ If a test charge moving with a velocity $\overrightarrow{v} = v_0 (3 \hat{i}- \hat{j} +2 \hat{k})$ experiences no force in that region, then the electric field in the region, in $SI$ units, is :

Question

$\begin{array}{1 1}(1)\; \overrightarrow{E} = -v_0B_0 (3 \hat{i} - 2\hat{j} -4 \hat{k}) \\ (2)\; \overrightarrow{E} = -v_0B_0 (\hat{i} + \hat{j}+7 \hat{k}) \\ (3)\; \overrightarrow{E} = v_0B_0 (14 \hat{j} + 7\hat{k}) \\ (4)\; \overrightarrow{E} = -v_0B_0(14 \hat {j} + 7 \hat{k}) \end{array} $