Final answer:
None of the provided options correctly balances the chemical equation for the reaction between Ca3(PO4)2, SiO2, and C. The expected reaction and products seem to be for a different process involving calcium phosphate and water.
Step-by-step explanation:
To balance the initial chemical equation provided, none of the options (a, b, c, d) accurately represents the balanced reaction for the given reactants Ca3(PO4)2(s), SiO2(s), and C(s). However, it seems there's a mix-up with the provided options and the expected reaction. The correct balancing of the given equation needs an approach where each element's number of atoms is equal on both sides of the reaction. This involves determination of products, which are not given in the question. But, based on the information provided regarding calcium phosphate, water, and the dissolution of Ca3(PO4)2, a different type of reaction seems to be the subject of discussion.
If the question asked is indeed about the reaction between Ca3(PO4)2 and SiO2 with C, which is a typical industrial process to produce phosphorus, the balanced equation for that process would look different and typically involves the formation of calcium silicate (CaSiO3), carbon monoxide (CO), and phosphorus (P4).