d
According to question, as the test charge experiences no net force in that region i.e., sum of electric force \(\left( {{{\text{F}}_{\text{e}}} = {\text{q}}\overrightarrow {\text{E}} } \right)\,\) and magnetic forces \([{{\text{F}}_{\text{m}}} = {\text{q}}(\overline {\text{v}}  \times \overline {\text{B}} ]\) will be zero.  

Hence, \(F_{e}+F_{m}=0\)

\(\mathrm{F}_{\mathrm{e}}=-\mathrm{q}(\overline{\mathrm{v}} \times \overline{\mathrm{B}})\)

\(=-\mathrm{B}_{0} \mathrm{v}_{0}[(3 \hat{\mathrm{i}}-\hat{\mathrm{j}}+2 \hat{\mathrm{k}}) \times(\mathrm{i}+2 \hat{\mathrm{j}}-4 \hat{\mathrm{k}})]\)

\(=-B_{0} v_{0}(14 \hat{j}+7 \hat{k})\)