• # question_answer A charged particle moves with a constant velocity $(\hat{i}+\hat{j})\,\,m/s$ in a magnetic field $\vec{B}=(2\hat{i}+3\hat{k})\,T$and uniform electric field $\vec{E}=(a\hat{i}+b\hat{j}+c\hat{k})\,N/C,$ then (assuming all quantities in S.I. unit): A) $a=3$ B) $b=-\,3$ C) $c=-\,2$ D) ${{a}^{2}}+{{b}^{2}}+{{c}^{2}}=22$

$\vec{v}\times \vec{B}=-\vec{E}$ $(\hat{i}+\hat{j})\times (2\hat{i}+3\hat{k})=-\vec{E}$ $(-\,3\hat{i}+3\hat{j}+2\hat{k})=\vec{E}$