Exercise 12, § 5

Consider in $\mathbf{R}^3$, the closed convex cone C defined by the relations $\xi_1 \geq 0, \xi_2 \geq 0, \xi_3^2 \leq \xi_1 \xi_2$. Show that the line D of equations $\xi_1 = 0, \xi_3 = 1$ does not meet C, but that there is no plane through the origin 0 containing D and not meeting $C - \{ 0 \}$.