A positively charged particle projected towards east is deflected towards north by a magnetic field. In which direction the magnetic field may be ?

downwards

Right Hand Rule : 

Let east as X-Axis , North as Y-Axis and vertically upward as Z-axis.

$\vec{F} = q\vec{V}\times \vec{B}$

F Is along $\hat{j}$ , velocity is along $\hat{i}$ hence B must be along $-\hat{k}$