This research introduces the concept of an orthogonal set and explores the idea of orthogonality within the setting of a vector metric space. In addition, we provide fixed point theorems for the proposed concept and provide illustrated examples to demonstrate that our conclusions effectively generalize existing findings in the literature. In addition, the primary results are utilized to establish fixed point solutions for orthogonal in vector metric space. In addition, a unique and specific solution was created for the orthogonal shape in the vector space that we mentioned earlier. Finally, a solution to a problem was discovered through practical application.