Equation of the sphere described on the join of the points $\overline{\mathrm{a}}=2\overline{\mathrm{i}}+\overline{\mathrm{j}}-\overline{\mathrm{k}}$ and $\mathrm{b}=\overline{\mathrm{i}}-\overline{\mathrm{j}}+\overline{\mathrm{k}}$ as diameter, is

$$\begin{gathered} \overline{\mathrm{a}}=(2, 1, -1) \overline{\mathrm{b}}=(1, -1, 1) \\ \mathrm{eq} \mathrm{of} \mathrm{sphere} \\ (\mathrm{x}-2) (\mathrm{x}-1)+(\mathrm{y}-1) (\mathrm{y}+1)+(\mathrm{z}+1) (\mathrm{z}-1)=0 \\ {\mathrm{x}}^2-3\mathrm{x}+2+{\mathrm{y}}^2-1+{\mathrm{z}}^2-1=0 \\ {\mathrm{x}}^2+{\mathrm{y}}^2+{\mathrm{z}}^2-3\mathrm{x}=0 \\ {\overline{\mathrm{r}}}^2-\overline{\mathrm{r}}.3\overline{\mathrm{i}}=0 \end{gathered}$$