chemistry, polar or nonpolar

Why is NO3 nonpolar but CIF3 is polar? I looked at the lewis structures, they look similar, but why is one opposite.
also, when something is polar or non polar, my teacher said I should see which atom is more electronegativity is higher and draw arrows towards it on a lewis structure, then add "vectors"
What does that mean? can you explain the question above with vectors. I tried doing it and the vectors don't cancel for both of them, but apparently it does cancel for NO3.

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  1. 1. The NO3^- ion (I assume you just omitted the negative charge) is a trigonal planar molecule; therefore, the polar bonds between individual N and O cancel for the molecule due to the shape of the molecule; i.e., the molecule is symmetrical. The NO3^- is what we call an AB3 type molecule and that leads to it being trigonal planar. This site shows the structure but scroll through to the very bottom.
    http://www.molecularsoft.com/help/Chemical_Bonds-Lewis_Structure.htm The ClF3 molecule, however, is an AB3U2 type molecule with two unpaired sets of electrons and a geometry of trigonal bipyramidal. Here is a site that shows that.
    http://www.up.ac.za/academic/chem/mol_geom/t.htm
    Here the atoms also have individual polarity but the molecular symmetry does not cancel the polarity of the molecule.

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