Secure multiparty computation is an important research topic of cryptography and focus of the international cryptographic community. Many practical problems can be described using vectors. Therefore, it is of important theoretical and practical significance to study secure multiparty vector computation. Existing secure vector computation protocols are for integer vectors, and there are few works on rational vectors. To fill the gap, the secure multiparty computation is studied for rational vectors, including computing the dot product of two vectors, determining whether two vectors are equal, and whether one vector dominates another. The efficient protocols are proposed for these problems and the application of secure vector computation is extended. It is also proved that these new protocols are secure. The efficiency analysis shows that the proposed protocols outperform existing protocols. Finally, these new protocols are applied to solve some new vector computation problems and some computational geometric problems.