Question

A charged particle with charge q enters a region of constant ,uniform abd mutually orthogonal fields E vector and B vector with a velocity Vvector perpendicular to both E vector and B vector, and comes out without any change in magmituse or direction of V vector, then V vector will be in terms of B and E

Answer 1

Her E and B are orthogonal, which means they are perpendicular to each other.
here we have F[E] = F[B]
qE= qVB
E= VB
V= E/B which is equivalent to V= EX B / B^2 [ V= EBsin90/ B^2= E/B ]