Calculate the magnitude and direction of the electric field at the origin due to two charges?

To calculate the magnitude and direction of the electric field at the origin, we need to find the electric field vector due to each charge at the origin and then add them vectorially.

Step 1: Define the charges and their positions.
Charge $q_1 = 4.00 \text{ nc} = 4.00 \times 10^{-9} \text{ C}$ is at $P_1 = (0.600 \text{ m}, 0.800 \text{ m})$.
Charge $q_2 = +6.00 \text{ nc} = 6.00 \times 10^{-9} \text{ C}$ is at $P_2 = (0.600