International Journal of Neutrosophic Science IJNS 2690-6805 2692-6148 10.54216/IJNS https://www.americaspg.com/journals/show/1987 2020 2020 Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia Yaser Ahmad Alhasan University of Chinese Academy of Sciences, CAS, Mathematics Department, Beijing, China Lee Xu Deanship the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia Raja Abdullah Abdulfatah Deanship of the Preparatory Year, Prince Sattam bin Abdulaziz University, Alkharj, Saudi Arabia Abuobida M. Ahmed Alfahal The main goal of this paper is to study the geometrical characterization of the solutions for a vectorial equation defined in the twothree dimensional Euclidean spaces. The geometrical characterization of the solutions for the desired vectorial equation is obtained for many different values of t based on the circles and spheres in some generalizations of the real field, especially dual numbers, weak fuzzy complex numbers split-complex numbers, and complex numbers. 2023 2023 155 159 10.54216/IJNS.210415 https://www.americaspg.com/articleinfo/21/show/1987