Why is #NO_3# a non-polar molecule?
You mean NO3- I assume. It is non polar because it is a symmetrical trigonal planar structure.
I assume you mean NO3- (the nitrate anion); there is no NO3 molecule.
It is non-polar because it has a trigonal planar structure and the symmetry means that there is an even distribution of electron charge density over the three N - O bonds. Whilst we often draw the structure of NO3 as a Lewis structure comprising double and single bonds, the reality is that the three N-O bonds are actually identical. The delocalised electron system results from a combination formal charge with each oxygen carrying −2⁄3 of a charge, and the nitrogen carrying a +1 charge. Adding these up (3 x -2/3) + 1 = -1 which is the formal charge of the nitrate ion.