# Extension of Functional & Hahn-Banach

I am to illustrate a particular theorem by considering a functional f on $R^2$ defined by $f(x)=\alpha_1 \xi_1 + \alpha_2 \xi_2$, $x=(\xi_1,\xi_2)$, its linear extensions $\bar{f}$ to $R^3$ and the corresponding norms.
I think the norm of f is the sup|f(x)| over all x's in $R^2$ where, ||x||=1. And the norm of the extension is the sup| $\bar{f}(x)$| over all x's in $R^3$ where ||x||=1.