[UPSC CSE 2021] Electrostatics and Magnetostatics (Q54, 15M)

Given an infinite line charge of charge density 2\,\mathrm{nC\,m^{-1}} parallel to the y-axis and passing through the point (3,0,4)\,\mathrm{m} and an infinite sheet of charge of charge density 4\,\mathrm{nC\,m^{-2}} parallel to the x-y plane and passing through the point (0,0,6)\,\mathrm{m}. Calculate the electric field intensity at the point (10,10,10)\,\mathrm{m}. Assume free space.