1. Masalani bayon qilamiz: $X=\{y+z, x+z, x+y\}$ vektor maydon konform vektor maydonmi? 2. Konform vektor maydon uchun, vektor maydonning gradienti simmetrik va uning rotatsiyasi nol bo'lishi kerak. 3. Vektor maydonni $\mathbf{F} = (y+z, x+z, x+y)$ deb olamiz. 4. Rotatsiyani hisoblaymiz: $$\nabla \times \mathbf{F} = \left(\frac{\partial}{\partial y}(x+y) - \frac{\partial}{\partial z}(x+z), \frac{\partial}{\partial z}(y+z) - \frac{\partial}{\partial x}(x+y), \frac{\partial}{\partial x}(x+z) - \frac{\partial}{\partial y}(y+z)\right)$$ 5. Hisoblaymiz: $$\nabla \times \mathbf{F} = (1 - 1, 1 - 1, 1 - 1) = (0,0,0)$$ 6. Rotatsiya nol, demak vektor maydon konservativ (gradient) bo'lishi mumkin. 7. Endi gradient ekanligini tekshirish uchun, $\mathbf{F}$ ni gradient sifatida ifodalash mumkinligini ko'ramiz. 8. Agar $\mathbf{F} = \nabla \phi$, unda $$\frac{\partial \phi}{\partial x} = y+z, \quad \frac{\partial \phi}{\partial y} = x+z, \quad \frac{\partial \phi}{\partial z} = x+y$$ 9. Bu tenglamalarni integratsiya qilamiz: $$\phi = xy + xz + yz + C$$ 10. Shunday qilib, $\mathbf{F}$ gradient vektor maydon, ya'ni konform vektor maydon hisoblanadi. Javob: Ha, $X$ konform (gradient) vektor maydon.