To determine if a precipitate will form between NaCl, Na3PO4, and Ba(NO3)2, we need to check for possible precipitation reactions. Let's consider the possible reactions:

1. NaCl + Ba(NO3)2: No reaction occurs between NaCl and Ba(NO3)2. Both compounds are soluble in water and their ions (Na+, Cl-, Ba2+, and NO3-) will remain in solution.

2. Na3PO4 + Ba(NO3)2: This combination has the potential for precipitation. When aqueous solutions of Na3PO4 and Ba(NO3)2 are mixed, a double-replacement reaction can occur, resulting in the formation of Ba3(PO4)2 and NaNO3. Ba3(PO4)2 is a white, crystalline solid that is insoluble in water.

The balanced chemical equation for this precipitation reaction is:

3Ba(NO3)2(aq) + 2Na3PO4(aq) → Ba3(PO4)2(s) + 6NaNO3(aq)

Therefore, a precipitate of Ba3(PO4)2 will form when NaCl, Na3PO4, and Ba(NO3)2 are mixed.