A sheet of charge, ρs = -25 x 10^-25 C/m^2, intersects the x-axis @ x = 2, the y-axis @ y = 3, and the z-axis @ z = 4. Additionally a point charge of Q = 12.5 x 10^-6 C is located @ (-5, 2, 3). Find the resultant electric field due to the sheet and the point charge @ (-5, 10, 35).
E = (Q/4πε0R^2)*R/R
E = (ρs/2ε0)*aR
Sorry if they are difficult to read, first equation is generic Gauss' law for a point charge in unit vector notation and the second equation is Gauss' law for a sheet of charge in relation to a unit normal vector.
The Attempt at a Solution
I found the contribution of the point charge using the first equation (25.04j + 100.18k) and started on the plane charge. My guess would be to find the vector that passes through the point (-5, 10, 35), convert it to a unit vector and then multiply by (ρs/2ε0), but I don't know how to find the normal vector from the point and the plane equation. If there's another solution, please let me know. I've computed the plane equation to be: 6x + 4y + 3z= 12.
Any help is much appreciated!