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. 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.
    Here the atoms also have individual polarity but the molecular symmetry does not cancel the polarity of the molecule.

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