A particle at the origin of a Cartesian coordinate system carries a charge of \(3.89 \times 10^{-9} \mathrm{C}\). What are the magnitude and direction of the electric field at 

\((a)(4.00 \mathrm{~mm}, 0)\),

(b) \((0,4.00 \mathrm{~mm})\), and

(c) \((-2.829 \mathrm{~mm}, 2. 829 \mathrm{~mm})\) ?