When solutions of sodium phosphate and barium nitrate are mixed, the result is barium phosphate (as a precipitate) and sodium nitrate. The unbalanced equation is

[For each compound, construct a vector that lists the numbers of atoms of sodium (Na), phosphorus, oxygen, barium, and nitrogen. For instance, barium nitrate corresponds to (0, 0, 6, 1, 2).]

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Na3PO4 + Ba(NO3)2 → Ba3(PO4)2 + NaNO3