explain why N-O bond in NO2(subscript)minus shorter than N-O bond in NO3(sub)minus

Bond length increases with decreasing bond order. The nitrogen–oxygen bond order in NO₃^- is less than the nitrogen–oxygen bond order in NO₂^- (1.3 versus 1.5, respectively). Therefore, NO₃^- has longer nitrogen–oxygen bonds than does NO₂^-.

 

 

For reference :

 

The nitrate ion has three equivalent resonance structures.

There are four NO bonding pairs distributed over three NO bonding locations.